Sorry if this is in the wrong section. I just saw some other fourier qns in here so thought it might go in here.

Just need some homework help (not assessed)

So first part of the question is to write the coefficient c_n, of the periodic function,

f(t) = cos(1/2pi*t) for |t|< 1 and f(t) = 0 for 1<|t|< T/2, where T= period

so from the definition of c_n, i obtained the integral from [-1,1]

$\displaystyle c_n= 1/T \int cos(\frac{\pi}{2}t)e^{-inwt} dt $

by using integration by parts twice,

I arrived at

$\displaystyle c_n= \frac{1}{(4(inw)^2-\pi^2)T} (e^{inw}+e^{-inw}) =\frac{ 2cos(nw)}{(4(inw)^2-\pi^2)T}$

I am pretty sure this is correct ( Please correct me if iam wrong)

But the second question asks to wirte cos(pi/2t) in terms of complex exponentials and perform integration to find c_n as a function of w_n=(2pi)n/T and T.

I am not really sure what they are asking. Do they want me to find $\displaystyle \hat{f}(w_n)=Tc_n$?