How to get Fourier transform of rectangular window as shown by wvtool function?. Why frequency domain of rectwin(M) using fft and wvtool are different?

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rectangular window rectwin(M) is plotted in time domain and freuquency domain using wvtool.
But when I take fft of rectwin(M), it is giving the below result.
How to get the frequency domain as shown by wvtool?
WHy frequency domain of rectwin(M) using fft and wvtool are dfifferent?

Accepted Answer

Paul
Paul on 26 Jan 2022
Edited: Paul on 26 Jan 2022
It looks like wvtool is plotting the DTFT of rectwin(M)
[h,w] = freqz(rectwin(64),1);
figure
plot(w,db(abs(h)))
The DFT (as computed by fft() ), should be nonzero only at DC, and it is.
figure;
stem((0:63)/64*2*pi,abs(fft(rectwin(64))))
xlim([-0.1 2*pi])
How did you make your FFT plot?
As must be the case, the elements of the DFT are samples of the DTFT, as shown here plotted in absolute magnitude, not dB
figure
plot(w,(abs(h)))
hold on;
stem((0:63)/64*2*pi,abs(fft(rectwin(64))))
xlim([-0.1 pi])
  4 Comments
Paul
Paul on 31 Jan 2022
Still curious about this
E_HH = rand(90,45) + 1j*rand(90,45);
r = rectwin(90)*rectwin(45).';
isequal(E_HH,E_HH.*r)
ans = logical
1
So mutiplying E_HH by r should not have an effect on the results. But the images above are not the same, so there must be some other difference in the processing the led to those images.

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