Matched Filter for the signal x(t)=t*rect[(t-T/2)/T].

[LauraN]

Hello guys!
I'm an Italian girl. Can somebody help me to solve this exercise? I absolutely need it for my incoming exam.

I have to calculate the matched filter for the signal x(t)=t*rect[(t-T/2)/T].

I correctly solved other exercises like this so I know that first I have to calculate Fourier Transform X(f), then |X(f)|^2, then I have to calculate Fourier Inverse Transform of R(t)=|X(f)|^2 and eventually I calculate R(t-T).
I got the X(f), however I have huge problems to solve the next two steps, I'm not able to calculate Fourier Inverse Transform of |X(f)|^2.

Can somebody show me how to do, please?

 

[Ishuda]

Hello guys!
I'm an Italian girl. Can somebody help me to solve this exercise? I absolutely need it for my incoming exam.

I have to calculate the matched filter for the signal x(t)=t*rect[(t-T/2)/T].

I correctly solved other exercises like this so I know that first I have to calculate Fourier Transform X(f), then |X(f)|^2, then I have to calculate Fourier Inverse Transform of R(t)=|X(f)|^2 and eventually I calculate R(t-T).
I got the X(f), however I have huge problems to solve the next two steps, I'm not able to calculate Fourier Inverse Transform of |X(f)|^2.

Can somebody show me how to do, please?

Sometimes one can resort to tables of transforms to find the answer and work backward
https://en.wikipedia.org/wiki/Fourier_transform#Tables_of_important_Fourier_transforms