Existence oF Fourier Co-efficient

[Sultan Ahmed]

Homework Statement

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

Homework Equations

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 .

 

[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?