Frequency domain convolution vs Time domain multiplication

Hi, I want to smooth PSD. What I think is I calculated aurocorrelation via xcorr. Then I calculated fourier transform vit fft. Then convolved with gaussian windows. I get smoothed PSD.

According to fourier transform property instead of convolution, I can calculate ifft of PSD(which equal to autocorrelation) and ifft of gaussian window. I can multiply in time domain and I can calculate fourier transform. When I use this way I couldn't get smoothed PSD. Where is the problem?

Answer 1

[Image Analyst]

It should be that way. Are you sure the Gaussian was wide enough in the spatial domain and narrow enough in the spectral domain to notice any difference? Try different widths.