Coefficient quantization error recovery

Abstract

A novel method to recover perfect reconstruction (PR), after error caused by filter bank coefficient quantization is presented. At the moment, most work involving the design of two channel filter banks with signed-powers-of-two coefficients proposes to minimize the peak reconstruction error and/or the peak stop band ripple; the exact filter is never known. In this paper a new result is presented, showing that we can CSD code the coefficients of a filter bank and regain PR via a post-processing filter. This permits fast multiplier-less computation of the analysis or synthesis filter banks, while the end user can recover PR if desired by post-processing. We show that the coded synthesis and analysis polyphase matrices multiply to a diagonal matrix. The diagonal entries define a filter which can be inverted to obtain PR. The result applies to any filter bank.