Tracking Analysis of an Adaptive Notch Filter with Constrained Poles and Zeros

Peter Handel; Arye Nehorai

doi:10.1109/78.275602

Tracking Analysis of an Adaptive Notch Filter with Constrained Poles and Zeros

Peter Handel, Arye Nehorai

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Abstract

This paper analyzes the asymptotic tracking proper- ties of an adaptive notch filter (ANF) with pole-zero constraints [1] for the cancellation or retrieval of multiple time-varying sine waves in additive noise. The asymptotic mean square error (MSE) is analyzed using the methods of Ljung and Gunnarsson [2] when the variations in the underlying frequencies are assumed to be sufficiently small. Closed-form expressions for the MSE are derived as functions of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables. Computer simulations confirm the validity of the derived results.

Original language	English
Pages (from-to)	281-291
Number of pages	11
Journal	IEEE Transactions on Signal Processing
Volume	42
Issue number	2
DOIs	https://doi.org/10.1109/78.275602
State	Published - Feb 1994

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title = "Tracking Analysis of an Adaptive Notch Filter with Constrained Poles and Zeros",

abstract = "This paper analyzes the asymptotic tracking proper- ties of an adaptive notch filter (ANF) with pole-zero constraints [1] for the cancellation or retrieval of multiple time-varying sine waves in additive noise. The asymptotic mean square error (MSE) is analyzed using the methods of Ljung and Gunnarsson [2] when the variations in the underlying frequencies are assumed to be sufficiently small. Closed-form expressions for the MSE are derived as functions of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables. Computer simulations confirm the validity of the derived results.",

author = "Peter Handel and Arye Nehorai",

note = "Funding Information: Manuscript received October 22, 1991; revised January 25, 1993. The associate editor coordinating the review of this paper and approving it for publication was Dr. James Zeidler. This work was supported by the Air Force Office of Scientific Research under Grant AFOSR-90-0164 and by the Office of Naval Research under Grant NOOO14-91-J-1298. P. Hbdel is with the Systems and Control Group, Uppsala University, Uppsala, Sweden. A. Nehorai is with the Department of Electrical Engineering, Yale University, New Haven, CT 06520. IEEE Log Number 9214194.",

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N2 - This paper analyzes the asymptotic tracking proper- ties of an adaptive notch filter (ANF) with pole-zero constraints [1] for the cancellation or retrieval of multiple time-varying sine waves in additive noise. The asymptotic mean square error (MSE) is analyzed using the methods of Ljung and Gunnarsson [2] when the variations in the underlying frequencies are assumed to be sufficiently small. Closed-form expressions for the MSE are derived as functions of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables. Computer simulations confirm the validity of the derived results.

AB - This paper analyzes the asymptotic tracking proper- ties of an adaptive notch filter (ANF) with pole-zero constraints [1] for the cancellation or retrieval of multiple time-varying sine waves in additive noise. The asymptotic mean square error (MSE) is analyzed using the methods of Ljung and Gunnarsson [2] when the variations in the underlying frequencies are assumed to be sufficiently small. Closed-form expressions for the MSE are derived as functions of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables. Computer simulations confirm the validity of the derived results.

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Tracking Analysis of an Adaptive Notch Filter with Constrained Poles and Zeros

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