On Adaptive Filtering in Oversampled Subbands

Weiss, S. (1998) On Adaptive Filtering in Oversampled Subbands. University of Strathclyde, Electrical & Electronic Engineering, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

For a number of applications like acoustic echo cancellation, adaptive filters are required to identify very long impulse responses. To reduce the computational cost in implementations, adaptive filtering in subband is known to be beneficial. Based on a review of popular fullband adaptive filtering algorithms and various subband approaches, this thesis investigates the implementation, design, and limitations of oversampled subband adaptive filter systems based on modulated complex and real valued filter banks. The main aim is to achieve a computationally efficient implementation for adaptive filter systems, for which fast methods of performing both the subband decomposition and the subband processing are researched. Therefore, a highly efficient polyphase implementation of a complex valued modulated generalized DFT (GDFT) filter bank with a judicious selection of properties for non-integer oversampling ratios is introduced. By modification, a real valued single sideband modulated filter bank is derived. Non-integer oversampling ratios are particularly important when addressing the efficiency of the subband processing. Analysis is presented to decide in which cases it is more advantageous to perform real or complex valued subband processing. Additionally, methods to adaptively adjust the filter lengths in subband adaptive filter (SAF) systems are discussed. Convergence limits for SAFs and the accuracy of the achievable equivalent fullband model based on aliasing and other distortions introduced by the employed filter banks are explicitly derived. Both an approximation of the minimum mean square error and the model accuracy can be directly linked to criteria in the design of the prototype filter for the filter bank. Together with an iterative least-squares design algorithm, it is therefore possible to construct filter banks for SAF applications with pre-defined performance limits. Simulation results are presented which demonstrate the validity and properties of the discussed SAF methods and their advantage over fullband and critically sampled SAF systems.

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