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Filter Design for dsPIC MCU Digital Filter Design and Analysis System for use with Microchip Technology dsPIC Microcontrollers
Momentum Data Systems, Inc.
Copyright/Trademark Information Copyright 2002 Momentum Data Systems 17330 Brookhurst Street, Suite 230 Fountain Valley, CA 92708 World rights reserved. No part of this publication may be stored in a retrieval system, transmitted, or reproduced in any way, including but not limited to photocopy, photograph, magnetic or other record, without the prior agreement and written permission of Momentum Data Systems. Information in this manual is subject to change without notice and does not represent a commitment on the part of Momentum Data systems. The software described in this reference guide is furnished under a license agreement and may be used or copied only in accordance with the of the agreement. This manual was produced and printed using FrameMaker. FrameMaker is a ed trademark of Adobe. All trademarks are copyrighted to their respective owners. Microchip, dsPIC, and MPLAB are trademarks of Microchip Technology Inc. and are used under license.
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Filter Design for Microchip dsPIC MCU Table of Contents Chapter 1
Introduction to Filter Design for Microchip Technology dsPIC MCU 1.1 Design Capabilities
1-2
1.2 General System Features. 1.3 Installation 1.3.1
1-5
Application Software Installation
1.4 Input Specifications 1.5 Design Methods
1-5
1-6
1-7
1.6 System Operation
Chapter 2
1-4
1-8
dsPIC Filter Design Examples 2.1 IIR Low
2-2
2.2 IIR Band 2-4 2.3 FIR Low
2-6
2.4 Equiripple FIR Low
Chapter 3
2-8
System Operation 3.1 Toolbar 3.1.1
3-3
Status Bar
3.2 File Menu 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7
3-6
Load Specification File 3-7 Print 3-8 Printer Setup 3-8 System Settings 3-9 Information 3-10 Exit 3-10 About dsPIC Filter Design
3.3 View Menu 3.3.1 3.3.2 3.3.3
3-13
3-14
IIR Design 3-15 FIR Design with Windows 3-17 Equiripple FIR Design 3-20
3.5 Filter Menu 3.5.1 3.5.2
3-11
3-12
Toolbar 3-12 Status Bar 3-12 Text Filter File View
3.4 Design Menu 3.4.1 3.4.2 3.4.3
3-5
3-22
Low 3-23 High 3-23
dsPIC Filter Design Reference Guide
Page i
3.5.3 3.5.4
Band 3-25 Bandstop 3-26
3.6 Output Menu 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7
3-27
Plot Control 3-27 Snap to Grid 3-30 Quantization 3-30 Create Specification File 3-31 Create Filter Coefficient File 3-32 Create Matlab File 3-32 Create Plot Data Files 3-33
3.7 Code Generation Menu 3.7.1 3.7.2 3.7.3
3.8 Window Menu 3.8.1 3.8.2
Chapter 4
3-34
Create C Code 3-35 C Code File Generation 3-35 Microchip dsPIC30 Code Generation
3-40
Select Plots 3-41 Display Control 3-41
Addendum 4.1 References
4-2
4.2 IIR Design Output Example
Page ii
4-3
dsPIC Filter Design Reference Guide
3-35
CHAPTER 1
Introduction to Filter Design for Microchip Technology dsPIC MCU
This manual is a reference guide to the Filter Design for dsPIC MCU ("dsPIC FD") specifically developed for use with Microchip Technology’s dsPIC30F 16-bit MCU Product Family. It is intended to explain the usage of the system and what the various screen displays and computer printouts mean. It is not intended to be a tutorial on digital signal processing since several excellent texts on the subject exist and it is assumed that the has had a certain amount of academic or professional exposure to the subject. Several references are given in Chapter 4, should more in-depth information be required. More advanced versions of QEDesign are also available. Please call Momentum Data Systems for further information. These systems significantly more powerful filter design techniques.
dsPIC Filter Design Reference Guide
Page 1 - 1
1.1 Design Capabilities Infinite Impulse Response Filter Design: •
Low, High, Band, and Bandstop Filters
•
Filter orders up to 10 for Low and High Filters
•
Filter orders up to 20 for Band and Bandstop Filters
•
Five Analog Prototype Filters are available: –Butterworth –Tschebyscheff –Inverse Tschebyscheff –Elliptic –Bessel
•
Digital Transformations are performed by the following method: –Bilinear Transformation Method
•
Reports show design details such as all transformations from normalized low filter to desired filter
Finite Impulse Response Filter Design: •
Design Method Selection –FIR Windows Design –FIR Equiripple Design (Parks-McClellan)
•
Low, High, Band, and Bandstop filters
•
An FIR filter can have up to 513 taps
•
Following window functions are ed: –Rectangular –Hanning (Hann) –Hamming –Triangular –Blackman –Exact Blackman –3 Term Cosine –3 Term Cosine with continuous 3rd Derivative –Minimum 3 Term Cosine –4 Term Cosine –4 Term Cosine with continuous 5th Derivative –Minimum 4 Term Cosine –Good 4 Term Blackman Harris
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dsPIC Filter Design Reference Guide
–Harris Flat Top –Kaiser –Dolph-Tschebyscheff –Taylor –Gaussian •
Reports show design details such as window coefficients and Impulse Response prior to multiplying by the window function
•
Filters are designed for a maximum gain of 1
Code Generation Features •
Choice of placement of coefficients in Program Space or Data Space
•
dsPIC30F Assembly Code
•
C wrapper/header code generation
Other General Features •
Graphical Output includes: –Magnitude Response vs. Frequency –Log Magnitude vs. Frequency –Phase Response vs. Frequency –Group Delay vs. Frequency –Impulse Response vs. Time (per sample) –Step Response vs. Time (per sample) –Pole and Zero Locations (IIR only)
dsPIC Filter Design Reference Guide
Page 1 - 3
1.2 General System Features.
Page 1 - 4
1.
Recycling of input for comparative analysis - input for a filter is retained until a new specification is called for. This allows various IIR designs to be compared with FIR window designs as well as FIR equiripple designs.
2.
Use of 64 bit floating point for all design calculations ensures that maximum accuracy is maintained for the design calculations. Certain critical calculations are carried out in 128 bit precision.
3.
Specification file which allows the retention and retrieval of filter specifications.
4.
Help screens for all data entry fields.
5.
Cursor tracking on all frequency domain plots. X and Y coordinates read out automatically as the cursor is tracked on the function by holding the mouse button down and dragging across the window as desired.
6.
Graphical Zooming is available.
dsPIC Filter Design Reference Guide
1.3 Installation 1.3.1 Application Software Installation The system is automatically installed by executing the following command at the DOS prompt or the run dialog.
:\setup Note: this executes SETUP.EXE on the cd which decompresses the files and installs the software group.
dsPIC Filter Design Reference Guide
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1.4 Input Specifications The magnitude specification of the band of a filter is given in the form -20log10(1.0-δ1) This assumes the magnitude range of the band is from [1-δ1,1], δ1>0. Stopband specifications are given in the form -20log10(δ2) Thus the magnitude of the stopband is from [0, δ2]. Note that: -20log10(1.0-δ1) and -20log10(δ2) are positive numbers. These values are often referred to as band ripple and stopband ripple, but a more accurate description would be maximum band attenuation and minimum stopband attenuation. These forms are used throughout all IIR and FIR designs for Low, High, Band and Bandstop Filters.
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dsPIC Filter Design Reference Guide
1.5 Design Methods For the IIR design, a normalized low analog transfer function is generated based on the given filter specifications. This normalized low analog transfer function is then transformed to an unnormalized analog transfer function (low,high,band or bandstop) via the analog frequency transformation formulae. Values for the frequency transformation are suitably chosen to compensate for the prewarping caused by the subsequent bilinear transformation. The unnormalized transfer functions for Low, High, Band and Bandstop Filters are then transformed to the digital domain via the bilinear transformation. Details of the transformations are printed in the output file SFIL.OUT. Output for each design will be accumulated in this file until it is printed. The filter characteristics including the impulse response are simulated via cascaded second order sections with the poles and zeros grouped using the L. B. Jackson algorithm1 to minimize stability problems. For the FIR design with windows, the number of taps in the filter are determined using the window calculation, again based on input specifications. The coefficients for the taps are then determined by using the Fourier series design techniques for computing the impulse response and the window coefficients. The Equiripple FIR design uses the Remez2 exchange algorithm to determine an optimal solution. The solution is optimal in the minimax sense - that is the maximum error over the entire frequency band is minimized. This produces equiripple results in both the band and stopband.
1. Jackson, L. B. Digital Filters and Signal Processing - see Addendum (8) 2. Jackson, L. B. Digital Filters and Signal Processing - see Addendum (8)
dsPIC Filter Design Reference Guide
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1.6 System Operation The dsPIC FD system was designed to be intuitively easy to use without sacrificing any of the powerful design capabilities required for a sophisticated engineering application. The top menu bar provides all the necessary options to design filters and will save previously inputted data thus allowing specifications to be changed with the minimum of effort. To alter a field, simply move the cursor into the relevant field using the mouse or Enter keys and re-enter the desired data. The menus and dialogs are largely self-explanatory, thus allowing the system to be used with the minimum of difficulty. The merely selects the desired option/s by following the menu and dialog prompts. All dialog boxes have a cancel box which will cause the system to revert to the previous dialog box. It is not necessary to input data in floating point format as the system will automatically convert integers to the correct format. For example, 5000, 5000., and 5E03 are all equally acceptable forms of input. To start the system: Double-click on the dsPIC FD icon to launch the system or enter the following command:
<\path\>qedite.exe
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dsPIC Filter Design Reference Guide
CHAPTER 2
dsPIC Filter Design Examples
The authors of dsPIC FD believe that the most efficient way to become familiar with the implementation and potential of the system is to step through the examples provided. The following pages contain examples of the various design methods and are organized in the following manner: DESIGN METHOD and PROBLEM STATEMENT TOGETHER WITH INPUT, OUTPUTS are SFIL.OUT (Analysis provided with each design) and PLOTS.
The examples implemented are: TABLE 2-1
Example Listing
Example
Filter Type
1
IIR Low (Tschebyscheff)
2
IIR Band (Elliptic)
3
FIR Low (Kaiser)
4
Equiripple FIR (Low)
dsPIC Filter Design Reference Guide
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2.1 IIR Low The first example is an IIR design with an inverse Tschebyscheff analog prototype.
FIGURE 2-1
Low Filter Specifications
The frequencies are specified in Hertz.
FIGURE 2-2
Select Analog Prototype and Filter Order
Inverse Tschebyscheff is selected for the analog prototype. The filter order will default to 5 unless overridden in this dialog box.
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dsPIC Filter Design Reference Guide
FIGURE 2-3
System Responses for Example 1
dsPIC Filter Design Reference Guide
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2.2 IIR Band This example is an IIR band filter with an Elliptic Analog prototype.
FIGURE 2-4
Band Filter Specifications
This filter has relatively narrow transition bands. The Elliptic filter design method will be significantly more efficient than other analog prototypes.
FIGURE 2-5
Select Analog Prototype and Filter Order
The elliptic filter design is selected and the default filter order of 8 is also selected.
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dsPIC Filter Design Reference Guide
FIGURE 2-6
System Responses for Example 2
dsPIC Filter Design Reference Guide
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2.3 FIR Low The same low filter specifications as in Example 1 are used for this FIR low filter.
FIGURE 2-7
Low Filter Specifications
Several window functions are available for FIR design. However, the Kaiser window function is usually selected for this type of design.
FIGURE 2-8
Select Window Function and Filter Order
The Kaiser window design is selected with a default order of 19. It appears from the filter orders that a rectangular window would be better. However, a rectangular window will not provide a design where the first sidelobe of the stopband will be less than 45 dB.
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dsPIC Filter Design Reference Guide
FIGURE 2-9
System Responses for Example 3
dsPIC Filter Design Reference Guide
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2.4 Equiripple FIR Low The same low filter specifications as in Examples 1 and 3 are used for this FIR low filter
FIGURE 2-10
Low Filter Specifications
The Equiripple design can make use of both ripple values in the design of the filter whereas the FIR design with windows cannot. The FIR design with windows uses the only one ripple value and will over design the other ripple value
FIGURE 2-11
Select Filter Order
Note that the filter order is 11 - much less than the Kaiser window design.
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dsPIC Filter Design Reference Guide
FIGURE 2-12
System Responses for Example 4
The magnitude plot for this design is considerably different than the magnitude plot for the Kaiser window design. The equiripple design makes use of the two ripple values and thus requires fewer taps or coefficients to achieve the desired design specifications
dsPIC Filter Design Reference Guide
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dsPIC Filter Design Reference Guide
CHAPTER 3
System Operation
System operation is controlled via the standard graphical interface of a main menu bar with pull-down menus and dialog boxes. The main menu bar consists of the following entries: TABLE 3-1
Main Menu Bar
Selection
Description
File
Allows loading of previously stored filter and analysis input specifications
View
View the design data and filter files
Design
Selection of Filter Design Options
Filter
Selection of Filter Types
Output
Selects plotting options and output files
Codegen
Generates dsPIC assembly code
Window
Standard Windows Operations to select output and graphical options
dsPIC Filter Design Reference Guide
Page 3 - 1
After the system has been started, the following screen will be displayed:
FIGURE 3-1
Start-Up Screen
The FILE, VIEW, DESIGN, FILTER, OUTPUT, CODEGEN and WINDOW menu items are covered in this chapter.
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dsPIC Filter Design Reference Guide
3.1 Toolbar The toolbar allows the to select the most commonly used features by button. The toolbar appears as follows:
FIGURE 3-2
Toolbar buttons
The buttons and equivalent Menu options are detailed below in the order in which they appear on the toolbar. Load Files
FILE/Load Filter Specification File About/Printer Options
FILE/About, FILE/Printer Plot Display Options
WINDOW/Cascade, WINDOW/Tile Design Type Options
DESIGN/IIR, DESIGN/FIR, DESIGN/Equiripple
dsPIC Filter Design Reference Guide
Page 3 - 3
Filter Types
FILTER/Low, FILTER/High, FILTER/Band, FILTER/Bandstop Quantization Option
OUTPUT/Quantization Start Design
FILTER/Start Design Output Options
OUTPUT/Create Filter Specification File, OUTPUT/Create Filter Coefficient File OUTPUT/Create C Code File, OUTPUT/Create Matlab File
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dsPIC Filter Design Reference Guide
3.1.1 Status Bar
FIGURE 3-3
Status Bar Display
The Status Bar which appears at the bottom of the screen displays the following information: Status Snap to Grid On/Off Q16 - Resolution
dsPIC Filter Design Reference Guide
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3.2 File Menu Select the file menu by placing the cursor over the word FILE, click and hold the selection by moving the cursor to the appropriate item in the drop-down menu, prior to releasing the mouse button. Note that the enabled options are listed in black with disabled options appearing in gray. The FILE menu appears as follows:
FIGURE 3-4
File Menu
Certainly the most powerful feature of this menu is the ability to automatically load previously stored specifications via FILE/Load Specifications.
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dsPIC Filter Design Reference Guide
3.2.1 Load Specification File If the FILE/Load Specifications option was selected, the following dialog box will be displayed.
FIGURE 3-5
Filter Specification File Selection
All filter specification files suffixed by .SPC will be displayed. A filter specification file can be created by selecting OUTPUT/Create Specification File after a filter design is complete. The dialog box corresponding to the current design method will be started automatically after a specification file is selected. If necessary, the design method will be changed to a method that can design the filter.
dsPIC Filter Design Reference Guide
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3.2.2 Print On completion of a filter design, filter plots can be printed. The print menu does not apply to text windows. Text files must be printed outside of QED Lite.
FIGURE 3-6
Print Selection
Note: hardcopy plots are always printed in black and white. 3.2.3 Printer Setup Select the desired printer setup. Note these parameters are not saved after the system exits.
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dsPIC Filter Design Reference Guide
FIGURE 3-7
Printer Selection
The printer setup box will vary according to the type of printer. 3.2.4 System Settings The system settings dialog box controls global aspects of dsPIC FD operations.
FIGURE 3-8
System Setting Options
dsPIC Filter Design Reference Guide
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•
Exit Mode: These options determine what information is retained on exiting the application.
•
Open a view window when a text file is created: If this option is selected, a View window is opened with the contents of the text file. This applies to all output files.
3.2.5 Information The text in the Information will be displayed on the graphical displays and printouts.
FIGURE 3-9
Information Screen
3.2.6 Exit Exits the application.
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dsPIC Filter Design Reference Guide
3.2.7 About dsPIC FD Filter Design Displays the current version number and technical information. Technical is available for customers subscribing to maintenance contracts - please our sales department for further information.
FIGURE 3-10
About Screen
dsPIC Filter Design Reference Guide
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3.3 View Menu The items for this menu are shown as follows:
FIGURE 3-11
View Menu Items
3.3.1 Toolbar This option toggles the Toolbar display on and off. 3.3.2 Status Bar This option toggles the Status Bar display on and off.
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dsPIC Filter Design Reference Guide
3.3.3 Text Filter File View All files can be read in text format. Simply select the file type by scrolling through the available file types. Text files cannot be printed within dsPIC FD.
FIGURE 3-12
Text Display
dsPIC Filter Design Reference Guide
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3.4 Design Menu This section describes the filter design capabilities of the system. •
Infinite Impulse Response (IIR) Design
•
Finite Impulse Response (FIR) Design
•
Equiripple FIR Design
The following menu is the primary means of starting the design of digital filters.
FIGURE 3-13
Design Menu
The various design methods and filter types will be discussed in some detail although, it should be noted, that some filter types are specific to a particular design method. An output file (SFIL.OUT) is automatically created showing detailed calculations for the designs.
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dsPIC Filter Design Reference Guide
3.4.1 IIR Design Selects the system design method to Infinite Impulse Response (IIR) design. IIR designs all have loops in the difference equations that implement the filters - that is the output value in a linear function of previous output values as well as current and previous input values. IIR designs are classical filter designs using analog design methods which transform the resulting S domain filter to a Z domain filter.
FIGURE 3-14
IIR Design Options
Filter Type IIR designs for Low, High, Band and Bandstop filters all use analog prototypes. After selecting “Next” on the IIR Design Menu the following dialog box will be displayed.
FIGURE 3-15
Estimated Filter Order/Analog Type
dsPIC Filter Design Reference Guide
Page 3 - 15
The estimated orders for the five types of analog filters are displayed. In selecting a filter type, one should bear in mind certain salient characteristics of these analog filters. The Butterworth filter is maximally flat in the band and exhibits no ripples in either the band or the stopband. The Tschebyscheff and Inverse Tschebyscheff exhibit a more rapid cutoff than the Butterworth filter, but at the expense of ripples in either the band or the stopband. The Tschebyscheff filter has its ripples in the band whereas the Inverse Tschebyscheff filter has its ripples in the stopband. The Elliptic filter has the sharpest cutoff from the band to the stopband, but has ripples in both the stopband and the band and has a higher nonlinearity in its phase response. These characteristics carry over to the digital form of the transfer function. The Bessel filter order is estimated using the Butterworth order calculation. This order is probably optimistic and some fine tuning is required. The Bessel filter does not have as sharp a roll-off as the Butterworth filter. The desired order is an optional field. If nothing is specified, then the order associated with the selected analog filter type is used. The desired order field can be any positive integer (must be a multiple of 2 for bandstop or band filters) and is not restricted to merely incrementing the filter order.
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dsPIC Filter Design Reference Guide
3.4.2 FIR Design with Windows Sets the system design method to Finite Impulse Response (FIR) Windows design. FIR designs produce a filter in which difference equations do not have loops - that is, the output value is a function only of current and previous input values. Previous output values are not part of these filter calculations. The Windows type of FIR design is done by forming a truncated Fourier Series to represent the desired frequency response and 'windowing' or multiplying the resulting coefficients element by element with a window function to reduce the Gibbs effect of truncating the Fourier series. The dsPIC FD system sets the filter coefficient symmetries such that all FIR filters have linear phase.
FIGURE 3-16
FIR Design Menu
The system allows the specification of both the band ripple and the stopband ripple for filters. However, for window designs, the system selects the minimum ripple (smallest in linear sense) and uses that value for both the stopband and band ripples. This restriction is an inherent mathematical restriction of the FIR window design. Select Window Function and Filter Order After the system accepts specifications for either Low, High, Band, or Bandstop, a dialog box similar to the following dialog box is displayed with the estimated order for each of the ed window functions. The dsPIC FD system defaults to the Kaiser Window. The desired filter length is optional --if left blank the system will set the number of taps equal to the estimate. The estimate can be overridden by any value from 2 to 513.
dsPIC Filter Design Reference Guide
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FIGURE 3-17
Select Window Function
In selecting a window function for a filter, the number of taps cannot be used as a sole decision factor. Most of the Windows have a fixed falloff to the first sidelobe of the stopband - this value is the stopband attenuation in the following table:
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dsPIC Filter Design Reference Guide
TABLE 3-2
Window Function Limitations
Window Function
Sidelobe Peak (dB)
Stopband Attenuation (dB)
Asymptotic Decay dB/Octave
Rectangular
-13.37
20.96
-6
Triangular
-27.31
25.70
-12
Hanning
-31.47
43.94
-18
Hamming
-43.19
54.17
-6
Blackman
-58.11
75.29
-18
Exact Blackman
-68.20
85.57
-6
3 Term Cosine
-62.05
79.16
-6
3 Term Cosine with Continuous 3rd Derivative
-46.74
61.36
-30
Minimum 3 Term Cosine
-71.48
86.40
-6
4 Term Cosine
-74.39
87.78
-6
4 Term Cosine with Continuous 5th Derivative
-60.95
77.03
-42
Minimum 4 Term Cosine
-98.17
115.55
-6
Harris Flat Top
-80.05
97.03
-6
Good 4 Term Blackman Harris
-81.76
99.78
-6
Kaiser Dolph-Tschebyscheff Taylor Gaussian
Selectable Selectable Selectable Selectable
-6 0 0 -6
For the Windows with fixed stopband attenuation longer filter lengths reduces the transition bandwidth. The rectangular window is essentially no windowing and illustrates the Gibbs effect on truncating a Fourier series. Windows marked as ‘Selectable’ allow variable falloff to the main sidelobe and variable transition bands.
dsPIC Filter Design Reference Guide
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3.4.3 Equiripple FIR Design Selecting this menu item will set the system design method to Equiripple FIR design. This method is also known as the Parks-McClellan algorithm.
FIGURE 3-18
Equiripple FIR Design Menu
The following design box will be displayed during the design calculations for Low, High, Band, and Bandstop filter designs. The estimated number of taps will be accepted as a default if a desired number of taps is not entered.
FIGURE 3-19
Design Options
The number of taps for Equiripple designs can be any number from 3 to 513. Equiripple FIR Filter Design Limitations System specifications in Equiripple design may not be met for a variety of reasons. The algorithm appears to terminate normally in these cases, but the results do not give the desired results. Typically the gain will exceed 1.0 even though this is the expected maximum gain. If the detailed magnitude and log magnitude report was requested, the values can be examined to see how far from the desired value the computations are.
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dsPIC Filter Design Reference Guide
Errors of this nature are usually caused by one of the following factors: 1.
Transition band too narrow
2.
Very narrow bands
3.
Very narrow stopbands
dsPIC Filter Design Reference Guide
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3.5 Filter Menu The following table displays the various type of filters and available design methods: TABLE 3-3
Filter Types Filter Type
Low High Band Bandstop
IIR Design
FIR Design
ü ü ü ü
ü ü ü ü
FIGURE 3-20
Filter Menu
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dsPIC Filter Design Reference Guide
3.5.1 Low The following dialog box appears if Low was selected from the DESIGN menu or FILTER/Low was selected. All fields are mandatory and a valid entry must be in each of them. Frequencies are in Hertz. The stopband and band frequencies must be less than the sampling frequency/2.
FIGURE 3-21
Low Filter Input Screen
The band frequency of a low filter must be less than the stopband frequency. The attenuation or ripple of the stopband and band is expressed in dB. While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. A typical range of values for band ripple or attenuation is 0.01dB to 3dB. A typical range of values for stopband ripple is 20dB to 100dB. The band ripple must be less than the stopband ripple. 3.5.2 High The following dialog box appears if High was selected from the DESIGN menu or FILTER/High was selected. The band frequency must be greater than the stopband frequency. Both the stopband frequency and the band frequency must be less than the sampling frequency/2. The band ripple or attenuation must be less than the stopband ripple. Typical values for band ripples range from .01dB to 3dB while typical values for the stopband ripple range from 20dB to 100dB. Furthermore, the band frequency of a high filter must be greater than the stopband frequency. The attenuation or ripple of the stopband and band is expressed in dB. While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. A typical range of values for band ripple or dsPIC Filter Design Reference Guide
Page 3 - 23
attenuation is 0.01dB to 3dB. A typical range of values for the stopband ripple is 20dB to 100dB.
FIGURE 3-22
High Filter Input Screen
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dsPIC Filter Design Reference Guide
3.5.3 Band The following dialog box appears if a band filter was selected. There are two frequencies for the band and two frequencies for the stopband. All frequencies must be less than the sampling frequency/2. The first band frequency must be less than the second band frequency and the first band frequency must be greater than the first stopband frequency. Similarly, the second band frequency must be less than the second stopband frequency. While both the band ripple and the stopband ripple are required, the filter order is determined for FIR design with Windows using the stopband ripple only. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. For an Equiripple design, the transition regions are set internally such that the transition regions are symmetric. This is required to design an acceptable equiripple band filter.
FIGURE 3-23
Band Filter
dsPIC Filter Design Reference Guide
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3.5.4 Bandstop The following dialog box appears if a Bandstop filter was selected on the DESIGN menu or FILTER/Bandstop was selected. This dialog box is virtually identical to the Band dialog box. However, different design rules apply •
The first band frequency must be less than the second band frequency and the first stopband frequency must be less than the second stopband frequency.
•
The first band frequency must be less than the first stopband frequency and the second stopband frequency must be less than the second band frequency.
While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design.
FIGURE 3-24
Bandstop Filter
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dsPIC Filter Design Reference Guide
3.6 Output Menu The OUTPUT menu contains a variety of options related to data output - graphical, hardcopy, or data files.
FIGURE 3-25
Output Menu
3.6.1 Plot Control Selecting OUTPUT/ Plot Control causes the following dialog box to be displayed:
dsPIC Filter Design Reference Guide
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FIGURE 3-26
Plot Parameter Screen
The Plot control dialog box allows the plotting limits to be changed for a specific filter . All of the Check Box options are global system settings. This means that the option once set will remain in effect until explicitly reset via this dialog box. The settings are not activated until the next replot. This means, for example, that to see the change from linear frequency scale to log frequency scale, the ‘Accept’ button must be selected to force a replot. •
Frequency Range The system defaults to a range of [0,fs/2] where fs is the sampling frequency. The purpose of the frequency selection is to allow one to narrow in on a transition area from band to stopband. However, it is not restricted to this. One can demonstrate the periodicity of the magnitude and phase response by specifying a range that is greater than [0,fs].
•
Magnitude Range The standard range of values for the magnitude plot is from zero to one. However, this can be changed to any value between 0 and 10. Typically this can be used to look at the band ripple characteristics or the stopband ripple.
•
Log Magnitude Range The standard range of values for the Log Magnitude plot is -100 dB to 0 dB and these can be changed to any values between -200dB and +10dB.
•
Number of Time Steps For the IIR design, the system by default will compute the impulse response and step response for 300 time steps. This can be overridden by entering a different number
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dsPIC Filter Design Reference Guide
in the field designated “# Time Steps”. A maximum value of 32,000 time steps is allowed. However, computing 32,000 time steps may take as much as five minutes to compute depending on the speed of the computer. •
Log Frequency Scale To select logarithmic frequency scale, place a check mark in this box. The default number of decades for a log frequency plot is 5. The lower limit of the frequency range will be reset to reflect the 5 decade range. Smaller ranges or different ranges can be selected by specifically setting frequency range values.
•
Grid Lines on Plots Grid lines will appear on all plots if selected, otherwise only tick marks on the axes will be available.
•
Sinc Interpolation If this option is on a sin x/x interpolator is used to calculate the impulse and step responses of FIR filters with lengths < 100. For short filters and anti-symmetric filters, this will make significant difference in the plots. Note: the sinc interpolation essentially simulates the effect of a D to A converter.
•
Compute Pole/Zero Locations The 'Compute Pole and Zero Locations' option applies only to system analysis. Clearing this option will turn the calculation of poles and zeros for the ratio of polynomials input off. This should be done if the root finder fails when trying to find roots of a high order polynomial.
•
Add Detailed Plot Values to Output Detailed reports are also available for Magnitude, Log10 Magnitude, Phase and Group Delay graphs. These reports are the values used in the plots and are appended to the file named SFIL.OUT if this entry is selected.
•
Change Plotting Ranges Automatically When this option is selected, the plotting ranges will automatically be set to the following values whenever the problem is changed:
TABLE 3-4
Plot Ranges
Option Frequency Magnitude Log Magnitude Number of time steps
Range 0 to fs/2 0 to 1 -100 to 0 300
If the design has been completed and just the plotting ranges are to be changed, then changes in these values will be reflected in the plots after selecting the done button. If the option is deselected then the values in the plotting ranges will be used for all subsequent plots even if the problem is changed. This allows fixed plotting ranges independent of problem definition.
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3.6.2 Snap to Grid This feature allows the to snap plots to a grid. Zooms are achieved by clicking with the right mouse button and then dragging the mouse to form a rectangle. Releasing the right button will cause the plot to be zoomed to that rectangle. If the Snap To Grid option is on, the largest rectangle formed by the gridlines which completely encloses the rectangle drawn by dragging the mouse, will be the new plot values. 3.6.3 Quantization If OUTPUT/Quantization is selected, the following dialog box is displayed, allowing the selection of either Transpoosed Canonic Second Order Sections, or Canonic Second Order Sections.
FIGURE 3-27
Quantization Option
Realization Type for Cascaded Sections •
Transposed Canonic Second Order Sections This is cascaded biquad sections. For cascaded biquad sections, the poles and zeros are paired to minimize the gain from any one section. This is done by pairing a pole with its nearest zero. The sections are then ordered by the radius of the poles with the smallest radius first. Scaling coefficients are computed so that the maximum output of any section is one in absolute value. The scaling coefficients are absorbed into the numerator coefficients of the transfer function. This procedure produces a final multiplier with a value of 1.0. The difference equations for section i are: w i1 ( n – 1 ) b i0 y---------(n) ------------------------= -----x ( n ) + k k k 2 2 2
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dsPIC Filter Design Reference Guide
w i1 ( n ) w i2 ( n – 1 ) b i1 a i1 ---------------- = ------x ( n ) + -----y ( n ) + -----------------------k k k k 2 2 2 2
(EQ 1)
w i2 ( n ) b i2 a i2 --------------- = ------x ( n ) + -----y( n) k k k 2 2 2 The output of section i is he input of section i + 1. •
Canonic Second Order Sections Cascaded canonic sections requires scaling down the input signal to the first section. This is due to the in the first summing node. This form of the difference equations results in a simpler implementation, However, scaling down the input reduces the Signal to Noise Ratio. The coefficients of the numerator sections are scaled such that the output of any order that feeds into the numerator coefficients. Unless the number of clock cycles is an important issue, it is recommended that transpose canonic sections be used. The difference equations for section i are: wi ( n ) b i1 b i2 ( n ) a i1 ------------ = x---------+ ------w ( n – 1 ) + -----w ( n – 1 ) + -----w (n – 2) k k k i k i k i 2 2 2 2 2 b i0 b i1 b i2 y(n) ---------= -----w ( n ) + -----w ( n – 1 ) + -----w (n – 2) k k i k k i 2 2 2 2
(EQ 2)
3.6.4 Create Specification File The dsPIC FD system allows a filter specification to be saved in a file. If this option is selected, a subsequent dialog box will request the file name. The file will be created with an SPC suffix.
FIGURE 3-28
Filter Specification File
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3.6.5 Create Filter Coefficient File
FIGURE 3-29
Filter Coefficient File
The dsPIC FD system allows filter coefficients to be saved in a file. If this option is selected, a subsequent dialog box will request the file name. The file will be created with an FLT suffix. 3.6.6 Create Matlab File To save a filter in Matlab file format, use the following screen:
FIGURE 3-30
Matlab File Specification
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dsPIC Filter Design Reference Guide
3.6.7 Create Plot Data Files The data which generates the current plots can be written to a set of files. This allows processing in other visualization or computational applications. All files will have the same prefix with differing suffixes.
FIGURE 3-31
Plot Data Files
Any IIR filter is saved as a product of second order sections. The file format is a matrix of size n x 6 where n is the number of sections. The gain value is absorbed in the first section. The file is a pure text file suitable for loading as a text file into Matlab. FIR filters are saved as a column vector where the order of the column is the filter length, the gain which is normally 1 is absorbed into the coefficients.
dsPIC Filter Design Reference Guide
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3.7 Code Generation Menu There are two Code Generation options - generating C Code or Microchip’s dsPIC30F assembly language code.
FIGURE 3-32
Code Generation Menu
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dsPIC Filter Design Reference Guide
3.7.1 Create C Code
Creates optimized C Code based on the ’s designs to a specified file. 3.7.2 C Code File Generation C Code can be created for any filter. A fully documented C program which can be used as either a subroutine or main program is generated. This C program uses two include files: qed_filt.c and qed_cgen.h. The filter routines are in qed_filt.c and the function prototypes and structure definitions are defined in qed_cgen.h. The generated C code is most appropriately used in a floating point DSP or a personal computer. 3.7.3 Microchip dsPIC30 Code Generation The dsPIC FD system s optimized assembly language code generation specifically for Microchip’s dsPIC30 processor. Select the dsPIC30 option as shown below.
dsPIC Filter Design Reference Guide
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FIGURE 3-33
Code Generation options
The dsPIC30 FD code generator always creates an assembler file, *.s, where the filename is specified by the in the file save dialog box. This file contains the assembly definition of the filter structure, the filter coefficients and a code fragment showing how to call the generalized filter routine. Assuming that the name entered in the file save dialog is "FilterName", the generated assembly file is "FilterName.s". The "Use General Subroutine" radio button specifies that the filter source routine to be used is one of the following: •
FIR_Filter.s (Used in the case of FIR Filters)
•
IIRT_Filter.s (Used in the case of Transposed IIR Filters)
•
IIRC_Filter.s (used in the case of Canonic IIR Filters)
These general routines reside in the dsPIC FD setup folder depending on the filter type chosen in dsPIC FD (FIR, IIR Transpose or IIR Canonic). The respective general subroutine along with the generated FilterName.s assembly file must be added to the MPLAB Integrated Development Environment (IDE) project. The general subroutines will use the filter structure and filter coefficients present in the generated FilterName.s file as inputs. The C files option allows creation of a C header file: FilterName.h. This file is automatically created if the C wrapper option is selected for simulation of the filter. Coefficients can be placed in X space or program space. Coefficients cannot be placed in Y space. The coefficient space selection is used to indicate where the coefficients need
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dsPIC Filter Design Reference Guide
to be stored. The generated assembly code structure for the filter has the information on whether X space or program space is used for coefficients. Optional Files: •
C Header File: FilterName.h This file creates the external reference from C to the assembly language filter structure for the specified filter. It also has a sample code fragment showing how to call the generalized filter routine.
•
C Wrapper: FilterName_sim.c, FilterName_sim.cmd, FilterName_make.bat This option generates a C program that creates FilterName_imresponse.dat. It also automatically builds the FilterName.h and FilterName_sim.cmd which is the command file for the command line simulator dsPIC30.exe. Run the batch file FilterName_make.bat to assemble, compile, link and execute the command line simulator.
•
M-File: FilterName_matlab.m or FilterName_octave.m This option generates a command file for use in either MATLAB or OCTAVE.
FIGURE 3-34
Examples of Files Created when both C wrapper and M FILE options are selected
The command file will generate a plot of the impulse response and the log magnitude frequency plot of the filter. The simulator batch file FilterName_sim.cmd must be run before executing either *.m file. This Matlab command file is not the same file generated by Output/Create Matlab File. This file is used to create a frequency response for the impulse response of the filter. The file created by Output/Create Matlab File is a data file with filter coefficients only. The simulator batch file creates FilterName_imresponse.dat. This file is required for execution of the *.m file.
dsPIC Filter Design Reference Guide
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FIGURE 3-35
Save dsPIC30 code
The following is an example of a sample code generated for an FIR filter. Note this text is contained at the bottom of the generated assembly file.
FIGURE 3-36
Sample Code
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dsPIC Filter Design Reference Guide
There are three filter routines and three initialization routines. These routine names are shown on the following table: TABLE 3-5
Table of Filter Routine Names File Name
Filter type
Filter Routine Name
Input Routine Name
FIR_Filter.s
FIR
_BlockFIRFilter
_FIRFilterInit
IIRT_Filter.s
Transposed IIR
_BlockIIRTransposeFilter
_IIR TransposeFilterInit
IIRC_Filter.s
Canonic IIR
_BlockIIRCanonicFilter
_IIRCanonicInit
The transpose IIR routine is the preferred choice for IIR filters (called form 1 in the quantization menu). This routine uses more instructions than the Canonic Routine (Form 2). However, it behaves significantly better for filters where the poles are close to the unit circle.
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3.8 Window Menu The WINDOW menu allows selection and control of the graphical displays. A list of all graphical displays are displayed at the bottom of the menu. The Cascade and Tile options are self-explanatory.
FIGURE 3-37
Window Menu
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dsPIC Filter Design Reference Guide
3.8.1 Select Plots Clicking the Select Plots option causes the following menu item to be displayed:
FIGURE 3-38
Plot Display Selection
Plots which have been deselected using the Cancel window button can be reselected using this dialog box. All selected plots are indicated by a check mark. 3.8.2 Display Control Allows the selection of color, font and line style for plots and prints (Note: hardcopy printouts are black and white only). The following dialog boxes are provided:
dsPIC Filter Design Reference Guide
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FIGURE 3-39
Color Selection
FIGURE 3-40
Font Selection
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dsPIC Filter Design Reference Guide
FIGURE 3-41
Line Style Selection
dsPIC Filter Design Reference Guide
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dsPIC Filter Design Reference Guide
CHAPTER 4
Addendum
dsPIC Filter Design Reference Guide
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4.1 References
Page 4 - 2
1.
Antoniou, Andreas. Digital Filter Analysis and Design: McGraw Hill, 1979
2.
Bernhardt, Paul A. Simplified Design of High Order Recursive Group Delay Filters, IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, No. 5, October 1980.
3.
Crochiere, R. E. & Rabiner L. R., Multirate Digital Signal Processing: Prentice Hall, 1983.
4.
Elliott Douglas F. Handbook of Digital Signal Processing Engineering Applications: Academic Press Inc, 1987.
5.
Harris F.J., On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proc. IEEE, Vol 66, No. 1, pp. 51-83, Jan 1978.
6.
Hogenauer, E. B. An Economical Class of Digital Filters for Decimation and Interpolation; IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, No. 2, April 1981.
7.
Jackson, L. B. Digital Filters and Signal Processing. Kluwer, 1986.
8.
Jayant, N. S. & Noll P. Digital Coding of Waveforms. Prentice Hall, 1984.
9.
Kaiser, J. F. Nonrecursive Digital Filter Design using the IO - SinH Window Function: Proceedings of IEEE International Symposium on Circuits and Systems, 1984.
10.
Nuttal A. H. Some Windows with Very Good Sidelobe Behavior, IEEE Trans. Acoust., Speech and Signal Processing, vol ASSP-29, No. 1, pp 84-91, Feb. 1981.
11.
Oppenheim, Alan V. & Shafer, Ronald W. Digital Signal Processing: Prentice Hall, 1975.
12.
Parks, T.W. & Burrus C.S. Digital Filter Design. John Wiley & Sons, Inc., 1987.
13.
Proakis John G & Manolakis Dimitris G. Digital Signal Processing Principles, Algorithms, and Applications. 2nd Edition. Macmillan Publishing, New York, 1992.
14.
Rabiner, Lawrence R & Gold, Bernard. Theory & Application of Digital Signal Processing: Prentice Hall, 1975.
15.
Roberts, Richard A & Mullis, Clifford T. Digital Signal Processing: Addison-Wesley, 1987.
16.
Webster R.J. On Qualifying Windows for FIR Filter Design, IEEE Trans. Acoust., Speech & Signal Processing, vol. ASSP-31, no. 1, pp 237-240, Feb. 1983.
17.
Charles Schuler and Mahesh Chugani. Digital Signal Processing: A Hands-On Approach: Glencoe/McGraw-Hill, 2003
dsPIC Filter Design Reference Guide
4.2 IIR Design Output Example Following is an example of design output for an IIR Band filter. The various parts are explained as follows, with arrows denoting the corresponding segments on the example shown in Figure 4.1 1.
Problem description or filter specification
2.
Normalized low transfer function N
H(z) = Hd
2
∏
b i0 s + b i1 s + b i2 ---------------------------------------2 s + a i1 s + a i2 i=1
(EQ 3)
Where N is the number of second order sections. 3.
Unnormalized analog transfer function U(s) formed by using analog frequency transformations for Low to Band in this example 2
2
s +ω s → ----------------0- Bs
(EQ 4)
where B is the bandwidth and ω0 is the center frequency. These values are prewarped for the bilinear transformation. Note: the order for the unnormalized transfer function U(s) doubles for a Low to Band transformation. U(s) is the product of the 2nd order sections. 4.
The digital transfer function H(z) formed from the unnormalized transfer function U(s) by applying the bilinear transformation H(z) is the product of the 2nd order sections. N
H ( z ) = Hd
∏ i=1
b i0 z 2 + b i1 + b i2 - = H d ------------------------------------ z 2 + a i1 + a i2
N
–1
–2
( b i0 + b i1 z + b i2 z ) --------------------------------------------------–1 –2 ( 1 + a i1 z + a i2 z ) i=1
∏
(EQ 5)
5.
The zeros of H(z)
6.
The poles of H(z)
7.
Numerator and Denominator of H(z) in powers of z.
8.
The maximum and minimum impulse response as calculated by simulating the filter response to an impulse input response.
dsPIC Filter Design Reference Guide
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FIGURE 4-1
IIR Band Filter
FILTER TYPE BAND ANALOG FILTER TYPE ELLIPTIC BAND RIPPLE IN -dB -1.0000 STOPBAND RIPPLE IN -dB -45.0000 BAND CUTOFF FREQUENCIES 900.000 1100.00 HERTZ STOPBAND CUTOFF FREQUENCIES 800.000 1200.00 HERTZ SAMPLING FREQUENCY 6000.00 HERTZ FILTER ORDER: 8 1 FILTER DESIGN METHOD: BILINEAR TRANSFORMATION NORMALIZED ANALOG TRANSFER FUNCTION T(s) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* 2 S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM .100000E+01 .000000E+00 .116352E+02 .100000E+01 .506146E+00 .166324E+00 .100000E+01 .000000E+00 .222240E+01 .100000E+01 .172643E+00 .512697E+00 INITIAL GAIN .293912143E-02 UNNORMALIZED ANALOG TRANSFER FUNCTION T(s) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM 3 .232838E+00 .000000E+00 .369783E+07 .100000E+01 .559404E+03 .427568E+08 .232838E+00 .000000E+00 .332854E+08 .100000E+01 .623399E+03 .530990E+08 .232838E+00 .000000E+00 .673253E+07 .100000E+01 .177624E+03 .374781E+08 .232838E+00 .000000E+00 .182819E+08 .100000E+01 .225823E+03 .605779E+08 INITIAL GAIN 1.00000000 DIGITAL TRANSFER FUNCTION Hd(z) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* Z**2 TERM Z TERM CONST TERM Z**2 TERM Z TERM CONST TERM 4 .3265918765 -.0023787440 .3265918765 1.00000 -.8886603703 .9268667712 .1924154175 -.3083779691 .1924154175 1.00000 -1.0466058250 .9306056718 .2499455221 -.1471073544 .2499455221 1.00000 -.8048919128 .9738539128 .2192763630 -.2918822351 .2192763630 1.00000 -1.1603089476 .9767824321 INITIAL GAIN 1.00000000 ZEROES OF TRANSFER FUNCTION Hd(z) 5 REAL PART IMAGINARY PART REAL PART IMAGINARY PART RADIUS .364176846E-02 .999993369E+00 .364176846E-02 -.999993369E+00 .100000000E+01 .801333836E+00 .598217422E+00 .801333836E+00 -.598217422E+00 .100000000E+01 .294278836E+00 .955719607E+00 .294278836E+00 -.955719607E+00 .100000000E+01 .665557909E+00 .746346213E+00 .665557909E+00 -.746346213E+00 .100000000E+01 POLES OF TRANSFER FUNCTION Hd(z) REAL PART IMAGINARY PART REAL PART IMAGINARY PART RADIUS .444330185E+00 .854071108E+00 .444330185E+00 -.854071108E+00 .962739202E+00 6 .523302913E+00 .810407141E+00 .523302913E+00 -.810407141E+00 .964679051E+00 .402445956E+00 .901050035E+00 .402445956E+00 -.901050035E+00 .986840368E+00 .580154474E+00 .800127002E+00 .580154474E+00 -.800127002E+00 .988323040E+00 NUMERATOR COEFFICIENTS - HIGHEST ORDER FIRST (in z) 7 .344415292E-02 -.121565672E-01 .271595297E-01 -.408909819E-01 .474622508E-01 -.408909819E-01 .271595297E-01 -.121565672E-01 .344415292E-02 DENOMINATOR COEFFICIENTS - HIGHEST ORDER FIRST (in z) 8 .100000000E+01 -.390046706E+01 .947529599E+01 -.147737178E+02 .170945309E+02 -.140611397E+02 .858318379E+01 -.336223066E+01 .820492586E+00 IMPULSE RESPONSE MIN = -.685317E-01, MAX = .680743E-01
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dsPIC Filter Design Reference Guide
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Filter Design for Microchip dsPIC MCU Table of Contents Chapter 1
Introduction to Filter Design for Microchip Technology dsPIC MCU 1.1 Design Capabilities
1-2
1.2 General System Features. 1.3 Installation 1.3.1
1-5
Application Software Installation
1.4 Input Specifications 1.5 Design Methods
1-5
1-6
1-7
1.6 System Operation
Chapter 2
1-4
1-8
dsPIC Filter Design Examples 2.1 IIR Low
2-2
2.2 IIR Band 2-4 2.3 FIR Low
2-6
2.4 Equiripple FIR Low
Chapter 3
2-8
System Operation 3.1 Toolbar 3.1.1
3-3
Status Bar
3.2 File Menu 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7
3-6
Load Specification File 3-7 Print 3-8 Printer Setup 3-8 System Settings 3-9 Information 3-10 Exit 3-10 About dsPIC Filter Design
3.3 View Menu 3.3.1 3.3.2 3.3.3
3-13
3-14
IIR Design 3-15 FIR Design with Windows 3-17 Equiripple FIR Design 3-20
3.5 Filter Menu 3.5.1 3.5.2
3-11
3-12
Toolbar 3-12 Status Bar 3-12 Text Filter File View
3.4 Design Menu 3.4.1 3.4.2 3.4.3
3-5
3-22
Low 3-23 High 3-23
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3.5.3 3.5.4
Band 3-25 Bandstop 3-26
3.6 Output Menu 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7
3-27
Plot Control 3-27 Snap to Grid 3-30 Quantization 3-30 Create Specification File 3-31 Create Filter Coefficient File 3-32 Create Matlab File 3-32 Create Plot Data Files 3-33
3.7 Code Generation Menu 3.7.1 3.7.2 3.7.3
3.8 Window Menu 3.8.1 3.8.2
Chapter 4
3-34
Create C Code 3-35 C Code File Generation 3-35 Microchip dsPIC30 Code Generation
3-40
Select Plots 3-41 Display Control 3-41
Addendum 4.1 References
4-2
4.2 IIR Design Output Example
Page ii
4-3
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3-35
CHAPTER 1
Introduction to Filter Design for Microchip Technology dsPIC MCU
This manual is a reference guide to the Filter Design for dsPIC MCU ("dsPIC FD") specifically developed for use with Microchip Technology’s dsPIC30F 16-bit MCU Product Family. It is intended to explain the usage of the system and what the various screen displays and computer printouts mean. It is not intended to be a tutorial on digital signal processing since several excellent texts on the subject exist and it is assumed that the has had a certain amount of academic or professional exposure to the subject. Several references are given in Chapter 4, should more in-depth information be required. More advanced versions of QEDesign are also available. Please call Momentum Data Systems for further information. These systems significantly more powerful filter design techniques.
dsPIC Filter Design Reference Guide
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1.1 Design Capabilities Infinite Impulse Response Filter Design: •
Low, High, Band, and Bandstop Filters
•
Filter orders up to 10 for Low and High Filters
•
Filter orders up to 20 for Band and Bandstop Filters
•
Five Analog Prototype Filters are available: –Butterworth –Tschebyscheff –Inverse Tschebyscheff –Elliptic –Bessel
•
Digital Transformations are performed by the following method: –Bilinear Transformation Method
•
Reports show design details such as all transformations from normalized low filter to desired filter
Finite Impulse Response Filter Design: •
Design Method Selection –FIR Windows Design –FIR Equiripple Design (Parks-McClellan)
•
Low, High, Band, and Bandstop filters
•
An FIR filter can have up to 513 taps
•
Following window functions are ed: –Rectangular –Hanning (Hann) –Hamming –Triangular –Blackman –Exact Blackman –3 Term Cosine –3 Term Cosine with continuous 3rd Derivative –Minimum 3 Term Cosine –4 Term Cosine –4 Term Cosine with continuous 5th Derivative –Minimum 4 Term Cosine –Good 4 Term Blackman Harris
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dsPIC Filter Design Reference Guide
–Harris Flat Top –Kaiser –Dolph-Tschebyscheff –Taylor –Gaussian •
Reports show design details such as window coefficients and Impulse Response prior to multiplying by the window function
•
Filters are designed for a maximum gain of 1
Code Generation Features •
Choice of placement of coefficients in Program Space or Data Space
•
dsPIC30F Assembly Code
•
C wrapper/header code generation
Other General Features •
Graphical Output includes: –Magnitude Response vs. Frequency –Log Magnitude vs. Frequency –Phase Response vs. Frequency –Group Delay vs. Frequency –Impulse Response vs. Time (per sample) –Step Response vs. Time (per sample) –Pole and Zero Locations (IIR only)
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1.2 General System Features.
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1.
Recycling of input for comparative analysis - input for a filter is retained until a new specification is called for. This allows various IIR designs to be compared with FIR window designs as well as FIR equiripple designs.
2.
Use of 64 bit floating point for all design calculations ensures that maximum accuracy is maintained for the design calculations. Certain critical calculations are carried out in 128 bit precision.
3.
Specification file which allows the retention and retrieval of filter specifications.
4.
Help screens for all data entry fields.
5.
Cursor tracking on all frequency domain plots. X and Y coordinates read out automatically as the cursor is tracked on the function by holding the mouse button down and dragging across the window as desired.
6.
Graphical Zooming is available.
dsPIC Filter Design Reference Guide
1.3 Installation 1.3.1 Application Software Installation The system is automatically installed by executing the following command at the DOS prompt or the run dialog.
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1.4 Input Specifications The magnitude specification of the band of a filter is given in the form -20log10(1.0-δ1) This assumes the magnitude range of the band is from [1-δ1,1], δ1>0. Stopband specifications are given in the form -20log10(δ2) Thus the magnitude of the stopband is from [0, δ2]. Note that: -20log10(1.0-δ1) and -20log10(δ2) are positive numbers. These values are often referred to as band ripple and stopband ripple, but a more accurate description would be maximum band attenuation and minimum stopband attenuation. These forms are used throughout all IIR and FIR designs for Low, High, Band and Bandstop Filters.
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1.5 Design Methods For the IIR design, a normalized low analog transfer function is generated based on the given filter specifications. This normalized low analog transfer function is then transformed to an unnormalized analog transfer function (low,high,band or bandstop) via the analog frequency transformation formulae. Values for the frequency transformation are suitably chosen to compensate for the prewarping caused by the subsequent bilinear transformation. The unnormalized transfer functions for Low, High, Band and Bandstop Filters are then transformed to the digital domain via the bilinear transformation. Details of the transformations are printed in the output file SFIL.OUT. Output for each design will be accumulated in this file until it is printed. The filter characteristics including the impulse response are simulated via cascaded second order sections with the poles and zeros grouped using the L. B. Jackson algorithm1 to minimize stability problems. For the FIR design with windows, the number of taps in the filter are determined using the window calculation, again based on input specifications. The coefficients for the taps are then determined by using the Fourier series design techniques for computing the impulse response and the window coefficients. The Equiripple FIR design uses the Remez2 exchange algorithm to determine an optimal solution. The solution is optimal in the minimax sense - that is the maximum error over the entire frequency band is minimized. This produces equiripple results in both the band and stopband.
1. Jackson, L. B. Digital Filters and Signal Processing - see Addendum (8) 2. Jackson, L. B. Digital Filters and Signal Processing - see Addendum (8)
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1.6 System Operation The dsPIC FD system was designed to be intuitively easy to use without sacrificing any of the powerful design capabilities required for a sophisticated engineering application. The top menu bar provides all the necessary options to design filters and will save previously inputted data thus allowing specifications to be changed with the minimum of effort. To alter a field, simply move the cursor into the relevant field using the mouse or Enter keys and re-enter the desired data. The menus and dialogs are largely self-explanatory, thus allowing the system to be used with the minimum of difficulty. The merely selects the desired option/s by following the menu and dialog prompts. All dialog boxes have a cancel box which will cause the system to revert to the previous dialog box. It is not necessary to input data in floating point format as the system will automatically convert integers to the correct format. For example, 5000, 5000., and 5E03 are all equally acceptable forms of input. To start the system: Double-click on the dsPIC FD icon to launch the system or enter the following command:
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dsPIC Filter Design Reference Guide
CHAPTER 2
dsPIC Filter Design Examples
The authors of dsPIC FD believe that the most efficient way to become familiar with the implementation and potential of the system is to step through the examples provided. The following pages contain examples of the various design methods and are organized in the following manner: DESIGN METHOD and PROBLEM STATEMENT TOGETHER WITH INPUT, OUTPUTS are SFIL.OUT (Analysis provided with each design) and PLOTS.
The examples implemented are: TABLE 2-1
Example Listing
Example
Filter Type
1
IIR Low (Tschebyscheff)
2
IIR Band (Elliptic)
3
FIR Low (Kaiser)
4
Equiripple FIR (Low)
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2.1 IIR Low The first example is an IIR design with an inverse Tschebyscheff analog prototype.
FIGURE 2-1
Low Filter Specifications
The frequencies are specified in Hertz.
FIGURE 2-2
Select Analog Prototype and Filter Order
Inverse Tschebyscheff is selected for the analog prototype. The filter order will default to 5 unless overridden in this dialog box.
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dsPIC Filter Design Reference Guide
FIGURE 2-3
System Responses for Example 1
dsPIC Filter Design Reference Guide
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2.2 IIR Band This example is an IIR band filter with an Elliptic Analog prototype.
FIGURE 2-4
Band Filter Specifications
This filter has relatively narrow transition bands. The Elliptic filter design method will be significantly more efficient than other analog prototypes.
FIGURE 2-5
Select Analog Prototype and Filter Order
The elliptic filter design is selected and the default filter order of 8 is also selected.
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dsPIC Filter Design Reference Guide
FIGURE 2-6
System Responses for Example 2
dsPIC Filter Design Reference Guide
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2.3 FIR Low The same low filter specifications as in Example 1 are used for this FIR low filter.
FIGURE 2-7
Low Filter Specifications
Several window functions are available for FIR design. However, the Kaiser window function is usually selected for this type of design.
FIGURE 2-8
Select Window Function and Filter Order
The Kaiser window design is selected with a default order of 19. It appears from the filter orders that a rectangular window would be better. However, a rectangular window will not provide a design where the first sidelobe of the stopband will be less than 45 dB.
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dsPIC Filter Design Reference Guide
FIGURE 2-9
System Responses for Example 3
dsPIC Filter Design Reference Guide
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2.4 Equiripple FIR Low The same low filter specifications as in Examples 1 and 3 are used for this FIR low filter
FIGURE 2-10
Low Filter Specifications
The Equiripple design can make use of both ripple values in the design of the filter whereas the FIR design with windows cannot. The FIR design with windows uses the only one ripple value and will over design the other ripple value
FIGURE 2-11
Select Filter Order
Note that the filter order is 11 - much less than the Kaiser window design.
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dsPIC Filter Design Reference Guide
FIGURE 2-12
System Responses for Example 4
The magnitude plot for this design is considerably different than the magnitude plot for the Kaiser window design. The equiripple design makes use of the two ripple values and thus requires fewer taps or coefficients to achieve the desired design specifications
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dsPIC Filter Design Reference Guide
CHAPTER 3
System Operation
System operation is controlled via the standard graphical interface of a main menu bar with pull-down menus and dialog boxes. The main menu bar consists of the following entries: TABLE 3-1
Main Menu Bar
Selection
Description
File
Allows loading of previously stored filter and analysis input specifications
View
View the design data and filter files
Design
Selection of Filter Design Options
Filter
Selection of Filter Types
Output
Selects plotting options and output files
Codegen
Generates dsPIC assembly code
Window
Standard Windows Operations to select output and graphical options
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After the system has been started, the following screen will be displayed:
FIGURE 3-1
Start-Up Screen
The FILE, VIEW, DESIGN, FILTER, OUTPUT, CODEGEN and WINDOW menu items are covered in this chapter.
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dsPIC Filter Design Reference Guide
3.1 Toolbar The toolbar allows the to select the most commonly used features by button. The toolbar appears as follows:
FIGURE 3-2
Toolbar buttons
The buttons and equivalent Menu options are detailed below in the order in which they appear on the toolbar. Load Files
FILE/Load Filter Specification File About/Printer Options
FILE/About, FILE/Printer Plot Display Options
WINDOW/Cascade, WINDOW/Tile Design Type Options
DESIGN/IIR, DESIGN/FIR, DESIGN/Equiripple
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Filter Types
FILTER/Low, FILTER/High, FILTER/Band, FILTER/Bandstop Quantization Option
OUTPUT/Quantization Start Design
FILTER/Start Design Output Options
OUTPUT/Create Filter Specification File, OUTPUT/Create Filter Coefficient File OUTPUT/Create C Code File, OUTPUT/Create Matlab File
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dsPIC Filter Design Reference Guide
3.1.1 Status Bar
FIGURE 3-3
Status Bar Display
The Status Bar which appears at the bottom of the screen displays the following information: Status Snap to Grid On/Off Q16 - Resolution
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3.2 File Menu Select the file menu by placing the cursor over the word FILE, click and hold the selection by moving the cursor to the appropriate item in the drop-down menu, prior to releasing the mouse button. Note that the enabled options are listed in black with disabled options appearing in gray. The FILE menu appears as follows:
FIGURE 3-4
File Menu
Certainly the most powerful feature of this menu is the ability to automatically load previously stored specifications via FILE/Load Specifications.
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dsPIC Filter Design Reference Guide
3.2.1 Load Specification File If the FILE/Load Specifications option was selected, the following dialog box will be displayed.
FIGURE 3-5
Filter Specification File Selection
All filter specification files suffixed by .SPC will be displayed. A filter specification file can be created by selecting OUTPUT/Create Specification File after a filter design is complete. The dialog box corresponding to the current design method will be started automatically after a specification file is selected. If necessary, the design method will be changed to a method that can design the filter.
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3.2.2 Print On completion of a filter design, filter plots can be printed. The print menu does not apply to text windows. Text files must be printed outside of QED Lite.
FIGURE 3-6
Print Selection
Note: hardcopy plots are always printed in black and white. 3.2.3 Printer Setup Select the desired printer setup. Note these parameters are not saved after the system exits.
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dsPIC Filter Design Reference Guide
FIGURE 3-7
Printer Selection
The printer setup box will vary according to the type of printer. 3.2.4 System Settings The system settings dialog box controls global aspects of dsPIC FD operations.
FIGURE 3-8
System Setting Options
dsPIC Filter Design Reference Guide
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•
Exit Mode: These options determine what information is retained on exiting the application.
•
Open a view window when a text file is created: If this option is selected, a View window is opened with the contents of the text file. This applies to all output files.
3.2.5 Information The text in the Information will be displayed on the graphical displays and printouts.
FIGURE 3-9
Information Screen
3.2.6 Exit Exits the application.
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dsPIC Filter Design Reference Guide
3.2.7 About dsPIC FD Filter Design Displays the current version number and technical information. Technical is available for customers subscribing to maintenance contracts - please our sales department for further information.
FIGURE 3-10
About Screen
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3.3 View Menu The items for this menu are shown as follows:
FIGURE 3-11
View Menu Items
3.3.1 Toolbar This option toggles the Toolbar display on and off. 3.3.2 Status Bar This option toggles the Status Bar display on and off.
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dsPIC Filter Design Reference Guide
3.3.3 Text Filter File View All files can be read in text format. Simply select the file type by scrolling through the available file types. Text files cannot be printed within dsPIC FD.
FIGURE 3-12
Text Display
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3.4 Design Menu This section describes the filter design capabilities of the system. •
Infinite Impulse Response (IIR) Design
•
Finite Impulse Response (FIR) Design
•
Equiripple FIR Design
The following menu is the primary means of starting the design of digital filters.
FIGURE 3-13
Design Menu
The various design methods and filter types will be discussed in some detail although, it should be noted, that some filter types are specific to a particular design method. An output file (SFIL.OUT) is automatically created showing detailed calculations for the designs.
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dsPIC Filter Design Reference Guide
3.4.1 IIR Design Selects the system design method to Infinite Impulse Response (IIR) design. IIR designs all have loops in the difference equations that implement the filters - that is the output value in a linear function of previous output values as well as current and previous input values. IIR designs are classical filter designs using analog design methods which transform the resulting S domain filter to a Z domain filter.
FIGURE 3-14
IIR Design Options
Filter Type IIR designs for Low, High, Band and Bandstop filters all use analog prototypes. After selecting “Next” on the IIR Design Menu the following dialog box will be displayed.
FIGURE 3-15
Estimated Filter Order/Analog Type
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The estimated orders for the five types of analog filters are displayed. In selecting a filter type, one should bear in mind certain salient characteristics of these analog filters. The Butterworth filter is maximally flat in the band and exhibits no ripples in either the band or the stopband. The Tschebyscheff and Inverse Tschebyscheff exhibit a more rapid cutoff than the Butterworth filter, but at the expense of ripples in either the band or the stopband. The Tschebyscheff filter has its ripples in the band whereas the Inverse Tschebyscheff filter has its ripples in the stopband. The Elliptic filter has the sharpest cutoff from the band to the stopband, but has ripples in both the stopband and the band and has a higher nonlinearity in its phase response. These characteristics carry over to the digital form of the transfer function. The Bessel filter order is estimated using the Butterworth order calculation. This order is probably optimistic and some fine tuning is required. The Bessel filter does not have as sharp a roll-off as the Butterworth filter. The desired order is an optional field. If nothing is specified, then the order associated with the selected analog filter type is used. The desired order field can be any positive integer (must be a multiple of 2 for bandstop or band filters) and is not restricted to merely incrementing the filter order.
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dsPIC Filter Design Reference Guide
3.4.2 FIR Design with Windows Sets the system design method to Finite Impulse Response (FIR) Windows design. FIR designs produce a filter in which difference equations do not have loops - that is, the output value is a function only of current and previous input values. Previous output values are not part of these filter calculations. The Windows type of FIR design is done by forming a truncated Fourier Series to represent the desired frequency response and 'windowing' or multiplying the resulting coefficients element by element with a window function to reduce the Gibbs effect of truncating the Fourier series. The dsPIC FD system sets the filter coefficient symmetries such that all FIR filters have linear phase.
FIGURE 3-16
FIR Design Menu
The system allows the specification of both the band ripple and the stopband ripple for filters. However, for window designs, the system selects the minimum ripple (smallest in linear sense) and uses that value for both the stopband and band ripples. This restriction is an inherent mathematical restriction of the FIR window design. Select Window Function and Filter Order After the system accepts specifications for either Low, High, Band, or Bandstop, a dialog box similar to the following dialog box is displayed with the estimated order for each of the ed window functions. The dsPIC FD system defaults to the Kaiser Window. The desired filter length is optional --if left blank the system will set the number of taps equal to the estimate. The estimate can be overridden by any value from 2 to 513.
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FIGURE 3-17
Select Window Function
In selecting a window function for a filter, the number of taps cannot be used as a sole decision factor. Most of the Windows have a fixed falloff to the first sidelobe of the stopband - this value is the stopband attenuation in the following table:
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dsPIC Filter Design Reference Guide
TABLE 3-2
Window Function Limitations
Window Function
Sidelobe Peak (dB)
Stopband Attenuation (dB)
Asymptotic Decay dB/Octave
Rectangular
-13.37
20.96
-6
Triangular
-27.31
25.70
-12
Hanning
-31.47
43.94
-18
Hamming
-43.19
54.17
-6
Blackman
-58.11
75.29
-18
Exact Blackman
-68.20
85.57
-6
3 Term Cosine
-62.05
79.16
-6
3 Term Cosine with Continuous 3rd Derivative
-46.74
61.36
-30
Minimum 3 Term Cosine
-71.48
86.40
-6
4 Term Cosine
-74.39
87.78
-6
4 Term Cosine with Continuous 5th Derivative
-60.95
77.03
-42
Minimum 4 Term Cosine
-98.17
115.55
-6
Harris Flat Top
-80.05
97.03
-6
Good 4 Term Blackman Harris
-81.76
99.78
-6
Kaiser Dolph-Tschebyscheff Taylor Gaussian
Selectable Selectable Selectable Selectable
-6 0 0 -6
For the Windows with fixed stopband attenuation longer filter lengths reduces the transition bandwidth. The rectangular window is essentially no windowing and illustrates the Gibbs effect on truncating a Fourier series. Windows marked as ‘Selectable’ allow variable falloff to the main sidelobe and variable transition bands.
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3.4.3 Equiripple FIR Design Selecting this menu item will set the system design method to Equiripple FIR design. This method is also known as the Parks-McClellan algorithm.
FIGURE 3-18
Equiripple FIR Design Menu
The following design box will be displayed during the design calculations for Low, High, Band, and Bandstop filter designs. The estimated number of taps will be accepted as a default if a desired number of taps is not entered.
FIGURE 3-19
Design Options
The number of taps for Equiripple designs can be any number from 3 to 513. Equiripple FIR Filter Design Limitations System specifications in Equiripple design may not be met for a variety of reasons. The algorithm appears to terminate normally in these cases, but the results do not give the desired results. Typically the gain will exceed 1.0 even though this is the expected maximum gain. If the detailed magnitude and log magnitude report was requested, the values can be examined to see how far from the desired value the computations are.
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dsPIC Filter Design Reference Guide
Errors of this nature are usually caused by one of the following factors: 1.
Transition band too narrow
2.
Very narrow bands
3.
Very narrow stopbands
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3.5 Filter Menu The following table displays the various type of filters and available design methods: TABLE 3-3
Filter Types Filter Type
Low High Band Bandstop
IIR Design
FIR Design
ü ü ü ü
ü ü ü ü
FIGURE 3-20
Filter Menu
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dsPIC Filter Design Reference Guide
3.5.1 Low The following dialog box appears if Low was selected from the DESIGN menu or FILTER/Low was selected. All fields are mandatory and a valid entry must be in each of them. Frequencies are in Hertz. The stopband and band frequencies must be less than the sampling frequency/2.
FIGURE 3-21
Low Filter Input Screen
The band frequency of a low filter must be less than the stopband frequency. The attenuation or ripple of the stopband and band is expressed in dB. While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. A typical range of values for band ripple or attenuation is 0.01dB to 3dB. A typical range of values for stopband ripple is 20dB to 100dB. The band ripple must be less than the stopband ripple. 3.5.2 High The following dialog box appears if High was selected from the DESIGN menu or FILTER/High was selected. The band frequency must be greater than the stopband frequency. Both the stopband frequency and the band frequency must be less than the sampling frequency/2. The band ripple or attenuation must be less than the stopband ripple. Typical values for band ripples range from .01dB to 3dB while typical values for the stopband ripple range from 20dB to 100dB. Furthermore, the band frequency of a high filter must be greater than the stopband frequency. The attenuation or ripple of the stopband and band is expressed in dB. While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. A typical range of values for band ripple or dsPIC Filter Design Reference Guide
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attenuation is 0.01dB to 3dB. A typical range of values for the stopband ripple is 20dB to 100dB.
FIGURE 3-22
High Filter Input Screen
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3.5.3 Band The following dialog box appears if a band filter was selected. There are two frequencies for the band and two frequencies for the stopband. All frequencies must be less than the sampling frequency/2. The first band frequency must be less than the second band frequency and the first band frequency must be greater than the first stopband frequency. Similarly, the second band frequency must be less than the second stopband frequency. While both the band ripple and the stopband ripple are required, the filter order is determined for FIR design with Windows using the stopband ripple only. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design. For an Equiripple design, the transition regions are set internally such that the transition regions are symmetric. This is required to design an acceptable equiripple band filter.
FIGURE 3-23
Band Filter
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3.5.4 Bandstop The following dialog box appears if a Bandstop filter was selected on the DESIGN menu or FILTER/Bandstop was selected. This dialog box is virtually identical to the Band dialog box. However, different design rules apply •
The first band frequency must be less than the second band frequency and the first stopband frequency must be less than the second stopband frequency.
•
The first band frequency must be less than the first stopband frequency and the second stopband frequency must be less than the second band frequency.
While both the band ripple and the stopband ripple are required, the filter order and results are determined using the stopband ripple only for FIR design with Windows. Both fields are required in case this specification is used in either an IIR design or an FIR Equiripple (Parks-McClellan) design.
FIGURE 3-24
Bandstop Filter
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3.6 Output Menu The OUTPUT menu contains a variety of options related to data output - graphical, hardcopy, or data files.
FIGURE 3-25
Output Menu
3.6.1 Plot Control Selecting OUTPUT/ Plot Control causes the following dialog box to be displayed:
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FIGURE 3-26
Plot Parameter Screen
The Plot control dialog box allows the plotting limits to be changed for a specific filter . All of the Check Box options are global system settings. This means that the option once set will remain in effect until explicitly reset via this dialog box. The settings are not activated until the next replot. This means, for example, that to see the change from linear frequency scale to log frequency scale, the ‘Accept’ button must be selected to force a replot. •
Frequency Range The system defaults to a range of [0,fs/2] where fs is the sampling frequency. The purpose of the frequency selection is to allow one to narrow in on a transition area from band to stopband. However, it is not restricted to this. One can demonstrate the periodicity of the magnitude and phase response by specifying a range that is greater than [0,fs].
•
Magnitude Range The standard range of values for the magnitude plot is from zero to one. However, this can be changed to any value between 0 and 10. Typically this can be used to look at the band ripple characteristics or the stopband ripple.
•
Log Magnitude Range The standard range of values for the Log Magnitude plot is -100 dB to 0 dB and these can be changed to any values between -200dB and +10dB.
•
Number of Time Steps For the IIR design, the system by default will compute the impulse response and step response for 300 time steps. This can be overridden by entering a different number
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in the field designated “# Time Steps”. A maximum value of 32,000 time steps is allowed. However, computing 32,000 time steps may take as much as five minutes to compute depending on the speed of the computer. •
Log Frequency Scale To select logarithmic frequency scale, place a check mark in this box. The default number of decades for a log frequency plot is 5. The lower limit of the frequency range will be reset to reflect the 5 decade range. Smaller ranges or different ranges can be selected by specifically setting frequency range values.
•
Grid Lines on Plots Grid lines will appear on all plots if selected, otherwise only tick marks on the axes will be available.
•
Sinc Interpolation If this option is on a sin x/x interpolator is used to calculate the impulse and step responses of FIR filters with lengths < 100. For short filters and anti-symmetric filters, this will make significant difference in the plots. Note: the sinc interpolation essentially simulates the effect of a D to A converter.
•
Compute Pole/Zero Locations The 'Compute Pole and Zero Locations' option applies only to system analysis. Clearing this option will turn the calculation of poles and zeros for the ratio of polynomials input off. This should be done if the root finder fails when trying to find roots of a high order polynomial.
•
Add Detailed Plot Values to Output Detailed reports are also available for Magnitude, Log10 Magnitude, Phase and Group Delay graphs. These reports are the values used in the plots and are appended to the file named SFIL.OUT if this entry is selected.
•
Change Plotting Ranges Automatically When this option is selected, the plotting ranges will automatically be set to the following values whenever the problem is changed:
TABLE 3-4
Plot Ranges
Option Frequency Magnitude Log Magnitude Number of time steps
Range 0 to fs/2 0 to 1 -100 to 0 300
If the design has been completed and just the plotting ranges are to be changed, then changes in these values will be reflected in the plots after selecting the done button. If the option is deselected then the values in the plotting ranges will be used for all subsequent plots even if the problem is changed. This allows fixed plotting ranges independent of problem definition.
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3.6.2 Snap to Grid This feature allows the to snap plots to a grid. Zooms are achieved by clicking with the right mouse button and then dragging the mouse to form a rectangle. Releasing the right button will cause the plot to be zoomed to that rectangle. If the Snap To Grid option is on, the largest rectangle formed by the gridlines which completely encloses the rectangle drawn by dragging the mouse, will be the new plot values. 3.6.3 Quantization If OUTPUT/Quantization is selected, the following dialog box is displayed, allowing the selection of either Transpoosed Canonic Second Order Sections, or Canonic Second Order Sections.
FIGURE 3-27
Quantization Option
Realization Type for Cascaded Sections •
Transposed Canonic Second Order Sections This is cascaded biquad sections. For cascaded biquad sections, the poles and zeros are paired to minimize the gain from any one section. This is done by pairing a pole with its nearest zero. The sections are then ordered by the radius of the poles with the smallest radius first. Scaling coefficients are computed so that the maximum output of any section is one in absolute value. The scaling coefficients are absorbed into the numerator coefficients of the transfer function. This procedure produces a final multiplier with a value of 1.0. The difference equations for section i are: w i1 ( n – 1 ) b i0 y---------(n) ------------------------= -----x ( n ) + k k k 2 2 2
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dsPIC Filter Design Reference Guide
w i1 ( n ) w i2 ( n – 1 ) b i1 a i1 ---------------- = ------x ( n ) + -----y ( n ) + -----------------------k k k k 2 2 2 2
(EQ 1)
w i2 ( n ) b i2 a i2 --------------- = ------x ( n ) + -----y( n) k k k 2 2 2 The output of section i is he input of section i + 1. •
Canonic Second Order Sections Cascaded canonic sections requires scaling down the input signal to the first section. This is due to the in the first summing node. This form of the difference equations results in a simpler implementation, However, scaling down the input reduces the Signal to Noise Ratio. The coefficients of the numerator sections are scaled such that the output of any order that feeds into the numerator coefficients. Unless the number of clock cycles is an important issue, it is recommended that transpose canonic sections be used. The difference equations for section i are: wi ( n ) b i1 b i2 ( n ) a i1 ------------ = x---------+ ------w ( n – 1 ) + -----w ( n – 1 ) + -----w (n – 2) k k k i k i k i 2 2 2 2 2 b i0 b i1 b i2 y(n) ---------= -----w ( n ) + -----w ( n – 1 ) + -----w (n – 2) k k i k k i 2 2 2 2
(EQ 2)
3.6.4 Create Specification File The dsPIC FD system allows a filter specification to be saved in a file. If this option is selected, a subsequent dialog box will request the file name. The file will be created with an SPC suffix.
FIGURE 3-28
Filter Specification File
dsPIC Filter Design Reference Guide
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3.6.5 Create Filter Coefficient File
FIGURE 3-29
Filter Coefficient File
The dsPIC FD system allows filter coefficients to be saved in a file. If this option is selected, a subsequent dialog box will request the file name. The file will be created with an FLT suffix. 3.6.6 Create Matlab File To save a filter in Matlab file format, use the following screen:
FIGURE 3-30
Matlab File Specification
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dsPIC Filter Design Reference Guide
3.6.7 Create Plot Data Files The data which generates the current plots can be written to a set of files. This allows processing in other visualization or computational applications. All files will have the same prefix with differing suffixes.
FIGURE 3-31
Plot Data Files
Any IIR filter is saved as a product of second order sections. The file format is a matrix of size n x 6 where n is the number of sections. The gain value is absorbed in the first section. The file is a pure text file suitable for loading as a text file into Matlab. FIR filters are saved as a column vector where the order of the column is the filter length, the gain which is normally 1 is absorbed into the coefficients.
dsPIC Filter Design Reference Guide
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3.7 Code Generation Menu There are two Code Generation options - generating C Code or Microchip’s dsPIC30F assembly language code.
FIGURE 3-32
Code Generation Menu
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dsPIC Filter Design Reference Guide
3.7.1 Create C Code
Creates optimized C Code based on the ’s designs to a specified file. 3.7.2 C Code File Generation C Code can be created for any filter. A fully documented C program which can be used as either a subroutine or main program is generated. This C program uses two include files: qed_filt.c and qed_cgen.h. The filter routines are in qed_filt.c and the function prototypes and structure definitions are defined in qed_cgen.h. The generated C code is most appropriately used in a floating point DSP or a personal computer. 3.7.3 Microchip dsPIC30 Code Generation The dsPIC FD system s optimized assembly language code generation specifically for Microchip’s dsPIC30 processor. Select the dsPIC30 option as shown below.
dsPIC Filter Design Reference Guide
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FIGURE 3-33
Code Generation options
The dsPIC30 FD code generator always creates an assembler file, *.s, where the filename is specified by the in the file save dialog box. This file contains the assembly definition of the filter structure, the filter coefficients and a code fragment showing how to call the generalized filter routine. Assuming that the name entered in the file save dialog is "FilterName", the generated assembly file is "FilterName.s". The "Use General Subroutine" radio button specifies that the filter source routine to be used is one of the following: •
FIR_Filter.s (Used in the case of FIR Filters)
•
IIRT_Filter.s (Used in the case of Transposed IIR Filters)
•
IIRC_Filter.s (used in the case of Canonic IIR Filters)
These general routines reside in the dsPIC FD setup folder depending on the filter type chosen in dsPIC FD (FIR, IIR Transpose or IIR Canonic). The respective general subroutine along with the generated FilterName.s assembly file must be added to the MPLAB Integrated Development Environment (IDE) project. The general subroutines will use the filter structure and filter coefficients present in the generated FilterName.s file as inputs. The C files option allows creation of a C header file: FilterName.h. This file is automatically created if the C wrapper option is selected for simulation of the filter. Coefficients can be placed in X space or program space. Coefficients cannot be placed in Y space. The coefficient space selection is used to indicate where the coefficients need
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dsPIC Filter Design Reference Guide
to be stored. The generated assembly code structure for the filter has the information on whether X space or program space is used for coefficients. Optional Files: •
C Header File: FilterName.h This file creates the external reference from C to the assembly language filter structure for the specified filter. It also has a sample code fragment showing how to call the generalized filter routine.
•
C Wrapper: FilterName_sim.c, FilterName_sim.cmd, FilterName_make.bat This option generates a C program that creates FilterName_imresponse.dat. It also automatically builds the FilterName.h and FilterName_sim.cmd which is the command file for the command line simulator dsPIC30.exe. Run the batch file FilterName_make.bat to assemble, compile, link and execute the command line simulator.
•
M-File: FilterName_matlab.m or FilterName_octave.m This option generates a command file for use in either MATLAB or OCTAVE.
FIGURE 3-34
Examples of Files Created when both C wrapper and M FILE options are selected
The command file will generate a plot of the impulse response and the log magnitude frequency plot of the filter. The simulator batch file FilterName_sim.cmd must be run before executing either *.m file. This Matlab command file is not the same file generated by Output/Create Matlab File. This file is used to create a frequency response for the impulse response of the filter. The file created by Output/Create Matlab File is a data file with filter coefficients only. The simulator batch file creates FilterName_imresponse.dat. This file is required for execution of the *.m file.
dsPIC Filter Design Reference Guide
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FIGURE 3-35
Save dsPIC30 code
The following is an example of a sample code generated for an FIR filter. Note this text is contained at the bottom of the generated assembly file.
FIGURE 3-36
Sample Code
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dsPIC Filter Design Reference Guide
There are three filter routines and three initialization routines. These routine names are shown on the following table: TABLE 3-5
Table of Filter Routine Names File Name
Filter type
Filter Routine Name
Input Routine Name
FIR_Filter.s
FIR
_BlockFIRFilter
_FIRFilterInit
IIRT_Filter.s
Transposed IIR
_BlockIIRTransposeFilter
_IIR TransposeFilterInit
IIRC_Filter.s
Canonic IIR
_BlockIIRCanonicFilter
_IIRCanonicInit
The transpose IIR routine is the preferred choice for IIR filters (called form 1 in the quantization menu). This routine uses more instructions than the Canonic Routine (Form 2). However, it behaves significantly better for filters where the poles are close to the unit circle.
dsPIC Filter Design Reference Guide
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3.8 Window Menu The WINDOW menu allows selection and control of the graphical displays. A list of all graphical displays are displayed at the bottom of the menu. The Cascade and Tile options are self-explanatory.
FIGURE 3-37
Window Menu
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dsPIC Filter Design Reference Guide
3.8.1 Select Plots Clicking the Select Plots option causes the following menu item to be displayed:
FIGURE 3-38
Plot Display Selection
Plots which have been deselected using the Cancel window button can be reselected using this dialog box. All selected plots are indicated by a check mark. 3.8.2 Display Control Allows the selection of color, font and line style for plots and prints (Note: hardcopy printouts are black and white only). The following dialog boxes are provided:
dsPIC Filter Design Reference Guide
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FIGURE 3-39
Color Selection
FIGURE 3-40
Font Selection
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dsPIC Filter Design Reference Guide
FIGURE 3-41
Line Style Selection
dsPIC Filter Design Reference Guide
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dsPIC Filter Design Reference Guide
CHAPTER 4
Addendum
dsPIC Filter Design Reference Guide
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4.1 References
Page 4 - 2
1.
Antoniou, Andreas. Digital Filter Analysis and Design: McGraw Hill, 1979
2.
Bernhardt, Paul A. Simplified Design of High Order Recursive Group Delay Filters, IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, No. 5, October 1980.
3.
Crochiere, R. E. & Rabiner L. R., Multirate Digital Signal Processing: Prentice Hall, 1983.
4.
Elliott Douglas F. Handbook of Digital Signal Processing Engineering Applications: Academic Press Inc, 1987.
5.
Harris F.J., On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proc. IEEE, Vol 66, No. 1, pp. 51-83, Jan 1978.
6.
Hogenauer, E. B. An Economical Class of Digital Filters for Decimation and Interpolation; IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, No. 2, April 1981.
7.
Jackson, L. B. Digital Filters and Signal Processing. Kluwer, 1986.
8.
Jayant, N. S. & Noll P. Digital Coding of Waveforms. Prentice Hall, 1984.
9.
Kaiser, J. F. Nonrecursive Digital Filter Design using the IO - SinH Window Function: Proceedings of IEEE International Symposium on Circuits and Systems, 1984.
10.
Nuttal A. H. Some Windows with Very Good Sidelobe Behavior, IEEE Trans. Acoust., Speech and Signal Processing, vol ASSP-29, No. 1, pp 84-91, Feb. 1981.
11.
Oppenheim, Alan V. & Shafer, Ronald W. Digital Signal Processing: Prentice Hall, 1975.
12.
Parks, T.W. & Burrus C.S. Digital Filter Design. John Wiley & Sons, Inc., 1987.
13.
Proakis John G & Manolakis Dimitris G. Digital Signal Processing Principles, Algorithms, and Applications. 2nd Edition. Macmillan Publishing, New York, 1992.
14.
Rabiner, Lawrence R & Gold, Bernard. Theory & Application of Digital Signal Processing: Prentice Hall, 1975.
15.
Roberts, Richard A & Mullis, Clifford T. Digital Signal Processing: Addison-Wesley, 1987.
16.
Webster R.J. On Qualifying Windows for FIR Filter Design, IEEE Trans. Acoust., Speech & Signal Processing, vol. ASSP-31, no. 1, pp 237-240, Feb. 1983.
17.
Charles Schuler and Mahesh Chugani. Digital Signal Processing: A Hands-On Approach: Glencoe/McGraw-Hill, 2003
dsPIC Filter Design Reference Guide
4.2 IIR Design Output Example Following is an example of design output for an IIR Band filter. The various parts are explained as follows, with arrows denoting the corresponding segments on the example shown in Figure 4.1 1.
Problem description or filter specification
2.
Normalized low transfer function N
H(z) = Hd
2
∏
b i0 s + b i1 s + b i2 ---------------------------------------2 s + a i1 s + a i2 i=1
(EQ 3)
Where N is the number of second order sections. 3.
Unnormalized analog transfer function U(s) formed by using analog frequency transformations for Low to Band in this example 2
2
s +ω s → ----------------0- Bs
(EQ 4)
where B is the bandwidth and ω0 is the center frequency. These values are prewarped for the bilinear transformation. Note: the order for the unnormalized transfer function U(s) doubles for a Low to Band transformation. U(s) is the product of the 2nd order sections. 4.
The digital transfer function H(z) formed from the unnormalized transfer function U(s) by applying the bilinear transformation H(z) is the product of the 2nd order sections. N
H ( z ) = Hd
∏ i=1
b i0 z 2 + b i1 + b i2 - = H d ------------------------------------ z 2 + a i1 + a i2
N
–1
–2
( b i0 + b i1 z + b i2 z ) --------------------------------------------------–1 –2 ( 1 + a i1 z + a i2 z ) i=1
∏
(EQ 5)
5.
The zeros of H(z)
6.
The poles of H(z)
7.
Numerator and Denominator of H(z) in powers of z.
8.
The maximum and minimum impulse response as calculated by simulating the filter response to an impulse input response.
dsPIC Filter Design Reference Guide
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FIGURE 4-1
IIR Band Filter
FILTER TYPE BAND ANALOG FILTER TYPE ELLIPTIC BAND RIPPLE IN -dB -1.0000 STOPBAND RIPPLE IN -dB -45.0000 BAND CUTOFF FREQUENCIES 900.000 1100.00 HERTZ STOPBAND CUTOFF FREQUENCIES 800.000 1200.00 HERTZ SAMPLING FREQUENCY 6000.00 HERTZ FILTER ORDER: 8 1 FILTER DESIGN METHOD: BILINEAR TRANSFORMATION NORMALIZED ANALOG TRANSFER FUNCTION T(s) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* 2 S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM .100000E+01 .000000E+00 .116352E+02 .100000E+01 .506146E+00 .166324E+00 .100000E+01 .000000E+00 .222240E+01 .100000E+01 .172643E+00 .512697E+00 INITIAL GAIN .293912143E-02 UNNORMALIZED ANALOG TRANSFER FUNCTION T(s) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM 3 .232838E+00 .000000E+00 .369783E+07 .100000E+01 .559404E+03 .427568E+08 .232838E+00 .000000E+00 .332854E+08 .100000E+01 .623399E+03 .530990E+08 .232838E+00 .000000E+00 .673253E+07 .100000E+01 .177624E+03 .374781E+08 .232838E+00 .000000E+00 .182819E+08 .100000E+01 .225823E+03 .605779E+08 INITIAL GAIN 1.00000000 DIGITAL TRANSFER FUNCTION Hd(z) NUMERATOR COEFFICIENTS DENOMINATOR COEFFICIENTS ************************************* ************************************* Z**2 TERM Z TERM CONST TERM Z**2 TERM Z TERM CONST TERM 4 .3265918765 -.0023787440 .3265918765 1.00000 -.8886603703 .9268667712 .1924154175 -.3083779691 .1924154175 1.00000 -1.0466058250 .9306056718 .2499455221 -.1471073544 .2499455221 1.00000 -.8048919128 .9738539128 .2192763630 -.2918822351 .2192763630 1.00000 -1.1603089476 .9767824321 INITIAL GAIN 1.00000000 ZEROES OF TRANSFER FUNCTION Hd(z) 5 REAL PART IMAGINARY PART REAL PART IMAGINARY PART RADIUS .364176846E-02 .999993369E+00 .364176846E-02 -.999993369E+00 .100000000E+01 .801333836E+00 .598217422E+00 .801333836E+00 -.598217422E+00 .100000000E+01 .294278836E+00 .955719607E+00 .294278836E+00 -.955719607E+00 .100000000E+01 .665557909E+00 .746346213E+00 .665557909E+00 -.746346213E+00 .100000000E+01 POLES OF TRANSFER FUNCTION Hd(z) REAL PART IMAGINARY PART REAL PART IMAGINARY PART RADIUS .444330185E+00 .854071108E+00 .444330185E+00 -.854071108E+00 .962739202E+00 6 .523302913E+00 .810407141E+00 .523302913E+00 -.810407141E+00 .964679051E+00 .402445956E+00 .901050035E+00 .402445956E+00 -.901050035E+00 .986840368E+00 .580154474E+00 .800127002E+00 .580154474E+00 -.800127002E+00 .988323040E+00 NUMERATOR COEFFICIENTS - HIGHEST ORDER FIRST (in z) 7 .344415292E-02 -.121565672E-01 .271595297E-01 -.408909819E-01 .474622508E-01 -.408909819E-01 .271595297E-01 -.121565672E-01 .344415292E-02 DENOMINATOR COEFFICIENTS - HIGHEST ORDER FIRST (in z) 8 .100000000E+01 -.390046706E+01 .947529599E+01 -.147737178E+02 .170945309E+02 -.140611397E+02 .858318379E+01 -.336223066E+01 .820492586E+00 IMPULSE RESPONSE MIN = -.685317E-01, MAX = .680743E-01
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dsPIC Filter Design Reference Guide
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