Fourier Transform: Solve Homework Equations for fd

[Lengalicious]

Homework Statement

See Attachment

Homework Equations

The Attempt at a Solution

Ok so in a previous question I worked out f_d = e^-ipd*2*sinc(pa)/√(2∏), also worked out its Fourier transform if that helps.

Now I really am stuck on the question, any guidance would be appreciated, I don't understand how the function f_d is summed over from -N to N, like I say any help to just send me in the right direction would be great.

 

[MisterX]

The problem suggests that the function f_d should be a function of x, but I don't see an x in your expression.

 

[Lengalicious]

The problem suggests that the function f_d should be a function of x, but I don't see an x in your expression.

Well the original function was f(x) which was a function of x that I then Fourier transformed with limits of x =-a to x=a, this replaced the x's with a's. f_d(x) was then a slight variation of the original f(x) function, ultimately I ended up with said function where f_d(x) = f(x - d) which transforms to e^(-ipd)*f(p) where f(p) was the Fourier transform of f(x).

 

[Lengalicious]

I made an issue with the question, not sure how to edit. Anyway f_d(x) = 1/a when |x-d|< a. What I said in the 1st post is actually the Fourier transform of this.