# Fourier series and limits

1. Sep 27, 2014

### ranju

1. The problem statement, all variables and given/known data
The major problem I am facing while solving for fourier series is about the limits to be taken while integrating..!!
In the general equation of fourier series the upper & lower limits are t1 & t1+T respectively..while solving for even functions we take t1 =-T/2..!! Why is it so..?? does this have something to do with the symmetry across y-axis??
In the 2 attached waveforms , in the first one , limits were like -pi to pi..while in 2nd limits are 0 to T/2.>!! I am not getting this..!!

2. Relevant equations

3. The attempt at a solution

The limits are t1 to t1+T whre T is the time period..but I am not getting how to decide value of t1..!!

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2. Sep 27, 2014

### Staff: Mentor

You have a function that is periodic with a period $T$. From the point of view of the theory, it makes no difference what value of $t_1$ you use, it will not affect the result (try it for yourself). Therefore, it is best to take the most convenient limits for the integration. If the function is even, using $t_1 = -T/2$ could save you from the full integral, by taking twice the integral from $t_1$ to $t_1 + T/2$.

The second case is somewhat similar to what I mentionned. Since the function is 0 for half the period, starting from 0 allows you to end at $T/2$, since the integral from $T/2$ to $T$ results in 0.

3. Sep 27, 2014

### ranju

Ohkk.. I have got the difference..! thanks for the help...