# Existence oF Fourier Co-efficient

1. Jan 31, 2012

### Sultan Ahmed

1. The problem statement, all variables and given/known data

Let f(t) be a signal whose time period is T.

1. if f(t+T/2)=f(t) proof that the fourier series representation will contain no odd harmonics
2. if f(t+T/2)=-f(t) proof that the fourier series representation will contain no even harmonics

2. Relevant equations

3. The attempt at a solution

1. I tried to proof that for f(t+T/2)=f(t) odd fourier co-efficient is zero . But I can not prove that .

2. Jan 31, 2012

### susskind_leon

You should write down the definition of the fourier series coefficients. Then take a good look at them and try to argue that they are 0 for odd numbers, given that f(t+T/2)=f(t). If you can't figure it out: what is the definition of the coefficients?