Adaptive Laguerre-lattice filters

Adaptive Laguerre-based filters provide an attractive alternative to adaptive FIR filters in the sense that they require fewer parameters to model a linear time-invariant system with a long impulse response. We present an adaptive Laguerre-lattice structure that combines the desirable features of the Laguerre structure (i.e., guaranteed stability, unique global minimum, and small number of parameters M for a prescribed level of modeling error) with the numerical robustness and low computational complexity of adaptive FIR lattice structures. The proposed configuration is based on an extension to the IIR case of the FIR lattice filter; it is a cascade of identical sections but with a single-pole all-pass filter replacing the delay element used in the conventional (FIR) lattice filter. We utilize this structure to obtain computationally efficient adaptive algorithms (O(M) computations per time instant). Our adaptive Laguerre-lattice filter is an extension of the gradient adaptive lattice (GAL) technique, and it demonstrates the same desirable properties, namely, (1) excellent steady-state behavior, (2) relatively fast initial convergence (comparable with that of an RLS algorithm for Laguerre structure), and good numerical stability. Simulation results indicate that for systems with poles close to the unit circle, where an (adaptive) FIR model of very high order would be required to meet a prescribed modeling error, an adaptive Laguerre-lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm.

[1]  Pertti M. Mäkilä,et al.  Approximation of stable systems by laguerre filters , 1990, Autom..

[2]  B. Friedlander,et al.  Lattice filters for adaptive processing , 1982, Proceedings of the IEEE.

[3]  B. Wahlberg.  System identification using Laguerre models , 1991 .

[4]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[5]  T. Oliveira e Silva,et al.  On the determination of the optimal pole position of Laguerre filters , 1995, IEEE Trans. Signal Process..

[6]  Alfred Fettweis.  The role of passivity and losslessness in multidimensional digital signal processing-new challenges , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[7]  G. A. Williamson.  Globally convergent adaptive filters with infinite impulse responses , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[9]  Phillip A. Regalia,et al.  Stable and efficient lattice algorithms for adaptive IIR filtering , 1992, IEEE Trans. Signal Process..

[10]  Nasir Ahmed,et al.  Optimum Laguerre networks for a class of discrete-time systems , 1991, IEEE Trans. Signal Process..

[11]  V. J. Mathews.  Adaptive polynomial filters , 1991, IEEE Signal Processing Magazine.

[12]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[13]  John E. Markel,et al.  Linear Prediction of Speech , 1976, Communication and Cybernetics.

[14]  David G. Messerschmitt,et al.  A class of generalized lattice filters , 1980 .

[15]  Charles W. Therrien,et al.  Discrete Random Signals and Statistical Signal Processing , 1992 .

[16]  J. Makhoul.  Stable and efficient lattice methods for linear prediction , 1977 .

[17]  I. Landau.  Unbiased recursive identification using model reference adaptive techniques , 1976 .

[18]  Charles R. Johnson,et al.  A convergence proof for a hyperstable adaptive recursive filter (Corresp.) , 1979, IEEE Trans. Inf. Theory.

[19]  W. Kautz.  Transient synthesis in the time domain , 1954 .

[20]  Fuyun Ling,et al.  Advanced Digital Signal Processing , 1992 .

[21]  C. Richard Johnson,et al.  Adaptive IIR filtering: Current results and open issues , 1984, IEEE Trans. Inf. Theory.

[22]  Thomas Kailath,et al.  Least-squares adaptive lattice and transversal filters: A unified geometric theory , 1984, IEEE Trans. Inf. Theory.