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I have signals captured from two channels of a measurement system. There is phase and magnitude differences between these two signals.

I want to apply nonlinear smoothing to the magnitude, but the phases should remain the same after the process.

This is what I have done both channels:

  1. Perform FFT
  2. calculate magnitude
  3. calculate phase
  4. apply nonlinear smoothing to the magnitude
  5. get real and imaginary part from smoothed magnitude and phase
  6. perform inverse FFT.

However the resultant signal is not as desired. It appears as a two sided time signal or has some additional signals in the end.

Is there a solution to this problem?

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  • $\begingroup$ Are you using a long enough FFT? The effect of the nonlinear smoothing of the magnitude could be like convolving the signal with a very long filter. If your signal is length $N$ and the effective length of the nonlinear smoothing is $M$, then your FFT needs to be of length $N+M-1$ (at least) to avoid circular convolution "aliasing". Examples of the sort of data you're using could also help, in addition to putting some numbers on the sizes of things (and perhaps the type of "nonlinear smoothing"). $\endgroup$
    – Peter K. ♦
    Commented Sep 24, 2013 at 16:34
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    $\begingroup$ Can you provide before/after pictures of the signal? What is the non-linear smoothing. With your reputation you won't be able to post the pictures here, but you can post them elsewhere and link to them here. $\endgroup$
    – Jim Clay
    Commented Sep 24, 2013 at 16:47

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Any smoothing in the frequency domain is similar to convolution filtering. And convolution filtering (with anything other an impulse or zero) will spread the width of a signal.

If you want a real result, you may need to check to make sure the input to your IFFT is conjugate symmetric.

If you don't want any phase shift, you could try copying the phase from before your filter into the result after your filtering and before the IFFT.

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  • $\begingroup$ Good point about keeping symmetry. I think the OP is already doing your last suggestion (they are only operating on the magnitude of the FFT, and keeping the phase). $\endgroup$
    – Peter K. ♦
    Commented Sep 24, 2013 at 20:01

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