State-space analysis of the adaptive notch filter

1 January 1986

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE

Vol. 74 (1) , 219-221
https://doi.org/10.1109/PROC.1986.13436

Abstract

The adaptive notch filter has a variety of applications in the field of communications including 60-Hz noise cancellation, phase-locked loops, frequency-hop filtering, and channel equalization. We present a simple derivation of the time-invariant state equations for the adaptive notch filter. Unlike previous work, this analysis provides a closed-form solution for the LMS weight vector as a rotated and filtered product of the desired response. This analysis also lends a simple explanation of non-Wiener type adaptive behavior.

Keywords

ADAPTIVE FILTERS
LEAST SQUARES APPROXIMATION
CLOSED-FORM SOLUTION
EQUATIONS
INFORMATION SYSTEMS
LABORATORIES
ALGORITHM DESIGN AND ANALYSIS
SYSTEMS ENGINEERING AND THEORY
TRANSFER FUNCTIONS
STATE-SPACE METHODS

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