A piloted adaptive notch filter

In the implementation of an adaptive notch filter using the least mean squares (LMS) algorithm, the zero of the filter is steered toward the input sinusoid based on the gradient information. The convergent may be speeded up if a larger step size is used when the zero of the notch filter is far away...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 53; no. 4; pp. 1310 - 1323
Main Authors: Yong Ching Lim, Yue Xian Zou, Zheng, N.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2005
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive algorithms
Adaptive filters
Adaptive notch filter
Algorithms
Applied sciences
Convergence
Cost engineering
Costs
Data mining
Detection, estimation, filtering, equalization, prediction
Estimates
Exact sciences and technology
fast convergence
Frequency estimation
Information filtering
Information filters
Information, signal and communications theory
Least mean square algorithms
least mean squares algorithm
Least squares approximation
low misadjustment
Notch filters
Notches
pilot notches
Pilots
Receivers & amplifiers
Sampling
Sampling methods
Sampling, quantization
Signal and communications theory
Signal, noise
steering direction
Studies
Telecommunications and information theory
variable step-size algorithm
Averaging method
Adaptive notch filter
low misadjustment
fast convergence
Information extraction
Adaptive filter
variable step-size algorithm
Algorithm
pilot notches
Implementation
Notch filter
Time domain method
Simulation
steering direction
Convergence rate
least mean squares algorithm
Sampling
Sinusoidal signal
Gradient method
Least mean squares methods
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Description
Summary:In the implementation of an adaptive notch filter using the least mean squares (LMS) algorithm, the zero of the filter is steered toward the input sinusoid based on the gradient information. The convergent may be speeded up if a larger step size is used when the zero of the notch filter is far away from the frequency of the input sinusoid. The gradient provides information on the direction where the zero should be steered but does not provide information on the distance between the zero and the frequency of the sinusoid. Conventional variable step-size algorithms determine the step size based on a (linear/nonlinear) weighted average of the gradient estimate at several sampling instances (time domain averaging). In this paper, we propose a new method for extracting information on the distance between the frequency of the input sinusoid and the zero of the notch. We use three (or more) notches, namely, a main notch and two (or more) pilot notches implemented with minimal additional cost. The pilot notches are used to analyze the gradient estimates at the same sampling instance but at several frequency points as the main notch. Simulation results show that our new piloted notch technique is significantly superior to step-size determination based on a time-averaging technique. Novel theoretical analysis is presented. Our method can be used in conjunction with most existing algorithms to determine the step size.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2005.843742