Tracking Analysis of Complex Adaptive IIR Notch Filter for a Linear Chirp Signal

Aloys MVUMA  Shotaro NISHIMURA  Takao HINAMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.6   pp.1526-1529
Publication Date: 2009/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1526
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
adaptive notch filter,  gradient algorithm,  linear chirp signal,  tracking MSE,  

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Summary: 
This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.