A tree-structured piecewise linear adaptive filter

Author

Gelfand, Saul B. ; Ravishankar, C.S.

Author_Institution

Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA

Volume

39

Issue

6

fYear

1993

fDate

11/1/1993 12:00:00 AM

Firstpage

1907

Lastpage

1922

Abstract

The authors propose and analyze a novel architecture for nonlinear adaptive filters. These nonlinear filters are piecewise linear filters obtained by arranging linear filters and thresholds in a tree structure. A training algorithm is used to adaptively update the filter coefficients and thresholds at the nodes of the tree, and to prune the tree. The resulting tree-structured piecewise linear adaptive filter inherits the robust estimation and fast adaptation of linear adaptive filters, along with the approximation and model-fitting properties of tree-structured regression models. A rigorous analysis of the training algorithm for the tree-structured filter is performed. Some techniques are developed for analyzing hierarchically organized stochastic gradient algorithms with fixed gains and nonstationary dependent data. Simulation results show the significant advantages of the tree-structured piecewise linear filter over linear and polynomial filters for adaptive echo cancellation

Keywords

adaptive filters; digital filters; echo suppression; estimation theory; linear network analysis; linear network synthesis; piecewise-linear techniques; trees (mathematics); adaptive echo cancellation; approximation properties; architecture; fast adaptation; filter coefficients; fixed gains; model-fitting properties; nodes; nonlinear adaptive filters; nonstationary dependent data; piecewise linear adaptive filter; polynomial filters; robust estimation; simulation results; stochastic gradient algorithms; training algorithm; tree-structured filter; tree-structured regression models; Adaptive filters; Algorithm design and analysis; Nonlinear filters; Performance analysis; Piecewise linear approximation; Piecewise linear techniques; Regression tree analysis; Robustness; Stochastic processes; Tree data structures;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.265499

Filename

265499