# Some Fourier series questions

1. Dec 3, 2008

### rforrevenge

1. The problem statement, all variables and given/known data
Recently in my signals class,we got to the chapter of Fourier series.We have learned that there are some basic graphs that can be described with Fourier series (sawtooth,square pulse etc) and so far i have understood their respective Fourier formulas.The problem i face though,is that when i have an exercise where i need to find the Fourier of a similar signal (i.e a shifted sawtooth wave),don't know how to do it.Here is a specific example:we have the fourier series for the sawtooth wave:x(t)=1/2-[00]\sum[n=1] (4/(2n-1)^2*pi ^2) cos {(2n-1)2pi/T *t} and the question is what are the Fourier coefficients for the sawtooth wave which starts from -0.1 and the max. point (amplitude) is 0.4.Below i have attached the graph of that signal.

P.S:Sorry for my poor English.I am really looking forward to the answer.

2. Relevant equations

3. The attempt at a solution
The professor told us that it can be solved using the Fourier properties.

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2. Dec 3, 2008

### wildman

First, I will assume your signal goes on forever in the same manner forever. This is a requirement for using the Fourier series. It only works on periodic signals. If what you show is all there is, you want to use a Fourier Transform. It works for aperiodic signals.

Given a periodic signal, the first thing you want to to is convert the saw tooth graph into a formula for x between -pi to pi (the period of the signal). See http://en.wikipedia.org/wiki/Fourier_series about half way down for a simple example. Your signal is a bit more complicated but it can be converted by breaking it into parts that can be integrated separately and then added together.

3. Dec 3, 2008

### turin

You can use Fourier series for signals of finite duration as long as you don't care what happens before or afterwards.