I would like to smooth amplitude spectra of signals around their peak frequencies. I could perform FFT, find the peak frequency, and smooth around the peak in frequency domain, then inverse FFT back to time domain. However, is there a way to do the spectrum smoothing in time domain? If finding peaking part is difficult, is there a time domain operator that smooths spectrum for a given frequency band? What would be the theory behind?

Thanks in advance.

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    $\begingroup$ Windowing in the time domain becomes filtering in the frequency domain. However if you intend to smooth the peaks on the Fourier magnitude, you introduce a nonlinearity $\endgroup$ – Laurent Duval Nov 7 '20 at 18:49
  • $\begingroup$ @LaurentDuval Windowing in the time domain reduces amplitude discontinuities at the boundaries of signals, thus reduces spectral leakage. Is that what you are refering when you say "windowing in the time domain becomes filtering in the frequency domain"? $\endgroup$ – sofname Nov 7 '20 at 19:30

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