An adaptive, high-order, notch filter using all pass sections

Abstract

A fully adaptive infinite impulse response notch filter in cascade form is proposed to detect and track multiple time-varying frequencies in additive white noise. Based on transformations for digital filters in the frequency domain, the filter results in a minimal number of parameters. In addition, a simple adaptive algorithm with good tracking and convergence properties is obtained by using all-pass filters and truncating the gradient. Computer simulations are included to verify the competitive performance of this filter under a wide range of conditions. From this analysis, we conclude that our new design is computationally simple, achieves rapid convergence, and is consequently a good choice in many non-stationary environments.