Cocept of FOURIER SERIES AND TRANSFORM

[bijaypaudel]

I am begineer student of signal analysis. I have problem understanding fourier series and its purpose. why we represent signal in sine and cosine form. Also help me regarding fourier transform and its uses. It will be gr8 it you give some applictions too..

 

[dean_winchester]

There are two things... one is periodic signal and one is non-periodic signal.
Well, the Fourier transform is for Non-Periodic signals while the fourier series is for a periodic signal. Non-Periodic means the period of a signal tends to infinity. Any signal can be represented in terms of sinusouidal signals.. that is why use of sin and cosine.
All real world signals can be represented as an infinite sum of sinusoidal functions via a Fourier series..

 

[bijaypaudel]

There is fourier transfer for periodic signals too...
Why do we need to represent signals in such a way...how does it help in analysis...
what types of signal processing can we do after fourier transform..
THIS IS WHAT I WANT TO KNOW....

 

[Mityan]

When you make a fourier transfor, you get a spectrumof signal. Forradicommunicationforexample you can see does you signal fit the channel you are given. You can estimate correlation of two signals much easier using fast fourier transform.
Jut try to open any book on signal processing.

 

[RCinFLA]

Yes, the fourier transform give the frequency spectrum of a time domain signal but there is a lot more magic that can be accomplished by some approximations and simplications of mathematics.

First an answer to your other question about why represent a waveform in sin and cos components. Look up Euler's identity.

One small example. Take amplitude modulation. Using the cos/sin quadrature format you can find the instantaneous value of the envelope by taking square root of the sum of cos component squared and sin component squared. Other types of modulation can be broken down similarly with quadrature components.

Back to fourier transforms. Shorten versions done in dig signal processors (FFT) can very closely fill in gaps in sampled data. A digital storage scope makes use of this by taking FFT over a sliding range of ADC samples to accurately extrapolate close approximations of points in between the samples. The FFT creates a sliding sinX/X series based on sample time period. These are summed in a sliding window to allow the digital scope to display points between the actual sample points.

There are many other things that can be done by doing FFT and inverse FFT's. You can clean up a photo by taking FFT's and filtering out certain rate of change components and enhancing others then inverse FFT's to get back an improved image.