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I am going through lecture slides on adaptive feedback cancellation right now, and several decorrelation measures are mentioned. As I understand, these are important in order to avoid a bias in filter estimation caused by correlation between system input and output coming through the feedback path.

The counter-measures listed in my slides are nonlinear operations to be added to the forward path on the error signal, namely

  • Frequency shift
  • Phase modulation
  • half wave rectifier

I am trying to understand how these work. For Band-limited signals, I assume the frequency shift is used because the cross-correlation corresponds to the multiplication of signal spectra, and the resulting cross-power density would be zero if the signal frequency components are shifted away from their original frequency range. In time domain, this should mean they are not correlated anymore.

What I do not understand, however, is how the other operations decorrelate signals in an adaptive feedback cancellation framework.

My questions are:

  • How does a phase modulation achieve a decorrelation effect and
  • How does a half wave rectifier achieve a decorrelation effect

in an AFC context?

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