Fourier Series(signal Processing) New 2c4o6t

Real world applications Of Fourier Series 1. Advanced noise cancellation and cell phones network technology

uses Fourier Series where digital filtering is used to minimize noise and bandwith demand respectively . 2. Many problems in physics involve vibrations and oscillations.

Often the oscillatory motion is simple (e.g. weights on springs, pendulums, harmonic waves etc.) and can be represented as single sine or cosine function However,in many cases, (electromagnetism, heat conduction, quantum theory,etc.) the wave forms are not simple and, unlike sines and cosines, can be difficult to treat analytically.Fourier methods give us a set of powerful tools for representing any periodic function as a sum of sines and cosines. 3. It can also be used for finding solutions of the heat equation.These

solutions have had a lot of applications in engineering. 4. Fourier series apply to periodic functions, and a generalisation is

the Fourier transform for general functions. You use the discrete Fourier transform every time you use wifi. 5. Another early use was in modelling and predicting ocean tides. 6. Most audio and images CODEC'S (including JPEG and Mp3)actually

use DCTs,which are a subset of generalized fourier transforms. 7. fourier series is broadly used in telecommunications system, for

modulation and demodulation of voice signals, also the input,output and calculation of pulse and their sine or cosine graph.

purpose of fourier series in signal processing In signal processing, the fourier transforms.often takes a time,& maps into a frequency spectrum i.e it takes the function from the time

domain into frequency domain Fourier series decomposes any periodic function or periodic signal into the sum of a set of simple oscillating functions i.e sines and cosines . A signal can be either continous or discrete & it can be either periodic or Aperiodic.these two features generates the four categories.

Types of fourier transforms 1. periodic-continous sines waves,square waves and another wavefrom that repeat itself in a regular pattern from negative to positive infinity ( this version of fourier transform is called the fourier series). 2. Aperiodic -continous for example, decaying exponentials and the Gaussian curve. These signals extend to both positive and negative infinity without repeating in a periodic pattern. this type of signal is simply called the Fourier Transform. 3.periodic discrete These are discrete signals that repeat themselves in a periodic fashion from negative to positive infinity. This is sometimes called the Discrete Fourier Series. 4.Aperiodic discrete These signals are only defined at discrete points between positive and negative infinity, and do not repeat themselves in a periodic fashion. This type of Fourier transform is called the Discrete Time Fourier Transform.