Question

Can any one Explain Fourier Series?

Answer 1

well HI first of all!
The idea is that any "function" can be viewed as a "signal" -- you can think of the independent variable x as the time, and the function f(x) as the signal at any given time.

Then what you do is break down the function in terms of frequencies. Any reasonable signal can be though of as, basically, a "sound" signal -- and all sounds are composed of frequencies.

So the Fourier series takes f(x) and transforms it into F(q) where F(q) tells you the strength of each frequency q in the signal f(x).

The mathematics of integration (calculus) tell you how to break down the signal and compute the frequencies. You can then decompose f(x) into its components of each frequency.

I hope that I have been able to explain this in plain language, without any confusing equations or symbols or anything -- those are important, but you can't learn them without understanding what it means, and hopefully the explanation I've given will help you with that. To start working on the technicals, I suggest MIT's open courses, or try reading Wikipedia (it can be helpful for a topic like Fourier series).

Answer 2

First of all a periodic signal, can be expressed as an infinite sum of sines and cosines Thus the function represented in one period is expressed as this infinite term. However, since doing anything with infinites sum is not practical, we approximate the infinite series by truncating it to contain some finite terms. This of course introduces an error between the actual signal(function) and the approximate signal. This error is minimum in the least square sense if we use the Fourier series. Further, with Fourier series, if we improve the approximation by including more terms, we need to calculate the strength due to added terms ony and what ever terms are there earlier will stay there in the same strength. This is the property of orthogonal function.