FRM-Based FIR Filters With Optimum Finite Word-Length Performance

It is well known that filters designed using the frequency response masking (FRM) technique have very sparse coefficients. The number of nontrivial coefficients of a digital filter designed using the FRM technique is only a very small fraction of that of a minimax optimum design meeting the same set of specifications. A digital filter designed using FRM technique is a network of several subfilters. Several methods have been developed for optimizing the subfilters. The earliest method optimizes the subfilters separately and produces a network of subfilters with excellent finite word-length performance. Subsequent techniques optimize the subfilters jointly and produce filters with significantly smaller numbers of nontrivial coefficients. Unfortunately, these joint optimization techniques, that optimize only the overall frequency response characteristics, may produce filters with undesirable finite word-length properties. The design of FRM-based filters that simultaneously optimizes the frequency response and finite word-length properties had not been reported in the literatures. In this paper, we develop several new optimization approaches that include the finite word-length properties of the overall filter into the optimization process. These new approaches produce filters with excellent finite word-length performance with almost no degradation in frequency response performance

I. Introduction

The Frequency Response Masking (FRM) technique [1]–[20] was developed for the synthesis of very sharp digital filters with very sparse coefficients. Thus, a filter synthesized using the FRM technique has very low complexity even though the effective filter length is slightly longer than that of the minimax optimum design meeting the same set of frequency response specifications. The FRM technique has been extended to the synthesis of various types of filters such as half-band filters [21]–[23], 2-D filters [24], IIR filters [25]–[28], filter banks [29]–[34], decimators and interpolators [35], [36], and Hilbert transformers [37], [38]. Implementations on various platforms [39]–[41] such as field-programmable gate array (FPGA) have also been investigated. Its applications in transmultiplexer design [42], ECG signal processing [43], hearing aids [44], digital audio [45]–[49] application and analysis, speech recognition [50], array beamforming [51], software radio [52], and noise thermometer [53] have also been reported.