a(x)=f-Nd(x) + f-(N-1)d(x) +...+ f(N-1)d(x) + fNd
fd(x) = (1/a for |x-d| < a and 0 otherwise)
Fourier transform of function g(x) is g~(p) = 1/root(2pi) ∫ dx e-ipx g(x)
The Attempt at a Solution
I have found the general Fourier transform for the function fd(x) and got:
f~(p) = root(2/pi) e-ipd sin(pa)/pa
I then tried to use the linearity of Fourier transform and added the solutions for f(x) but subbed in the various N, N-1 etc but got muddled up and a little confused.
Is this the right thing to be doing? Is this going to come out as a nice clean answer?
Thanks in advance.