On the periodically time-varying bias in adaptive feedback cancellation systems with frequency shifting

Frequency shifting has been used for acoustic feedback control in audio reinforcement systems since the 1950s. It can be used as a stand-alone system and/or it can be combined with an acoustic feedback cancellation system using adaptive filters. A spectral shifting of the loudspeaker signal in an audio system breaks the acoustic feedback loop, and it decorrelates the reference and error signals to the adaptive filter in the cancellation system, which is useful for getting an unbiased adaptive filter estimation. In this work, we analyze the decorrelation effect from the frequency shifting in an acoustic feedback cancellation system. We show that the influence from the frequency shifting, on the correlation function between the reference and error signals, can be divided into two parts: a fast time-varying part and a slowly time-varying part. Especially the slowly time-varying part of the correlation function leads to a periodically time-varying bias in the adaptive filter estimation, which limits the feedback cancellation performance. We propose a solution to obtain an unbiased estimation by removing the slowly time-varying part in the adaptive filter estimation and we verify it by simulations.