This is my first question on here so I'm new to the formatting and all so please be indulgent :)
I have an exam question where I am given a function H(f) that is a rectangular pulse between -fc and fc (where fc is a given frequency) of amplitude 1 and I need to calculate it's inverse Fourier transform. I've looked around online and could only find vague answers and not in the frequency domain.
Alternatively, if some of you want to think a little more, I have a given signal x(t) which is also a rectangular pulse between -d and d of amplitude A, I have it's frequency Fourier transform which is
X(f) = 2*A*d*sinc(2*pi*f*d)
I then have to convert x(t) into xp(t) where xp(t) is the periodic version of x(t) of period T and Xp(f) is the fourier transform of xp(t).
Assuming I now have xp(t), Xp(f) and H(f), the full question is:
We set xp(t) at the input of h(t), determine the range of frequencies fc such that the output signal y(t) is a sine function. To solve this I must either calculate a convolution of xp(t) and h(t) to get y(t) as a sine function or multiply Xp(f) and H(f), find Y(f) such that its inverse Fourier transform is a sine function.
I know that the fourier transform of a sine function is:
(1/2j)*[dirac(f-f0)-dirac(f+f0)]