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foldover effect in 2D FFT?

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Dean Ranmar
Dean Ranmar on 14 Nov 2016
Commented: Star Strider on 14 Nov 2016
I am simulating signal processing in a radar. When I place a simulated target in a known near-in range location in a range-Doppler map OR when I process actual data [offline] collected by a radar, I see some range-foldover effects. That is, when there is a distinct detectable target at near range, I also get detections at the same Doppler at far range. (I'm attaching portions of the code.) nfft pulses of rnfft range bins are received and form the initial R-Dop map. This is passed through a Matched Filter, then MTI, Pulse Doppler and inverse-MTI. A hamming window (weights) are applied in fast time (range - Matched Filter) and slow time (pulses - Pulse Doppler). I know this range-sidelobe effect is due to the Fourier transform in the Matched Filtering operation but, I'm not yet sure why it's there (the mechanism which causes it) or, how to counteract it [which I assume would follow from knowing why it happens.]
Suggestions?
Code portions:
cfdpcTempMat = conj(fft(dpcTemplateMat)); % conjugate FFT of MF template (with weighting)
rtrdMapRx is the range-Doppler map (rnfft range bins by nfft Doppler bins)
trRngDelayDpcMat = ifft(fft(rtrdMapRx).*cfdpcTempMat); % apply matched filter
trRngDelayDpcMtiMat = mtiMat * trRngDelayDpcMat.'; % apply mti window
trDpcDopMat = fft(dopWinMat*trRngDelayDpcMtiMat, nfft); % weight & pulse Doppler
trDpcDopImtiMat = imtiMat * trDpcDopMat; % spectrum equalizer based on inv mti
trDpcRngDopMap = abs(fftshift(trDpcDopImtiMat.',2)).^2; % shift freq 0 to center
(fftshift shifts zero velocity Doppler to center for convenience.)
  2 Comments
Dean Ranmar
Dean Ranmar on 14 Nov 2016
foldover due to fact fft (Fourier xform, in general) assumes sampled signal repeats (is periodic). therefore, it effectively folds near range over into far range, and vice versa.
thanks anyway for anyone who tried/tries to work on this ...........
Star Strider
Star Strider on 14 Nov 2016
It seems to me that you’re describing aliasing. Your Fourier transformed data are only correct to half the spatial frequency (the Nyquist frequency). So if your data are sampled at ‘n’ cycles/distance unit, your Fourier transform is only good to ‘n/2’ cycles/distance unit.
My experience with 2D Fourier transforms is negligible. I’m abstracting from my experience with 1D signal processing.

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