An Adaptive Algorithm with Variable Step-Size for Parallel Notch Filter

Yoshio ITOH

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A    No.2    pp.511-519
Publication Date: 2006/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.2.511
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
adaptive notch filter,  variable step-size,  convergence characteristics,  frequency estimation,  

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A parallel notch filter (PNF) for eliminating a sinusoidal signal whose frequency and phase are unknown, has been proposed previously. The PNF achieves both fast convergence and high estimation accuracy when the step-size for adaptation is appropriately determined. However, there has been no discussion of how to determine the appropriate step-size. In this paper, we derive the convergence condition on the step-size, and propose an adaptive algorithm with variable step-size so that convergence of the PNF is automatically satisfied. Moreover, we present a new filtering structure of the PNF that increases the convergence speed while keeping the estimation accuracy. We also derive a variable step-size scheme for the new PNF to guarantee the convergence. Simulation results show the effectiveness of the proposed method.