Understanding the full concept behind the fourier series

[v9260019]

hello all
i have a question about forier theorem
According to the Forier theorem, any practical periodic functon of frequency ω° can be expressed as an "infinite" sum of sine or cosine functions that are integral multiples of ω° ---------------why

thanks a lot

 

[Sathish]

Re: about forier theorem

To understand the full concept behind the fourier series draw the following steps what i say, Consider a square wave of 1Hz, over it draw a sine wave with 1Hz freq, and again draw a sine wave with 3Hz freq, and again draw a sine wave with 5Hz freq. Now you can see that the sum of the three sine wave can built a square wave(approximatelly. If the sine wave you drawn for 1Hz(fundamental),3Hz(3rd hormonics),5Hz(5th hormonic-the even hormonics are absent in this case) is extended for infinite you can exactly construct a 1Hz square. I hope you understand why you need to take an infinite sine terms for a fourier series.
This is a simple example for your understanding purpose

 

[alizadeh_m]

Re: about forier theorem

I did not understand the explanation. Could you explain more clearly the idea?

 

[LouisSheffield]

Re: about forier theorem

You can find a description here
https://mathworld.wolfram.com/FourierSeries.html
including graphs and such (and links for triangle, sawtooth and square waves).

It doesn't go much into the Gibbs phenomenon, which results from truncating the series prior to infinity, but that's also available as a separate link (at the bottom).