Design of recursive digital filters using frequency-response masking technique

Abstract

The implementation of recursive infinite impulse response (IIR) digital filters suffers from two problems: 1) the feedback loop in the IIR filters limits the opportunities for pipelined implementation, and 2) the coefficient sensitivity and roundoff noise of the IIR filters are very high when their transition bands are very narrow. This thesis presents new methods for designing high-speed pipelined IIR filters and IIR filters having low coefficient sensitivity and roundoff noise. The proposed methods are based on the frequency-response masking (FRM) technique. To design pipelined IIR filters using the FRM technique, the bandedge shaping filters are IIR filters whose feedback loop contains several delays and the masking filter are finite impulse response (FIR) filters. Both nonlinear phase and approximately linear phase FRM-based pipelined IIR filters are considered in the thesis. For the design of FRM-based pipelined IIR filters with nonlinear phase, we propose a novel two-stage FRM approach where the bandedge shaping filters in the second stage are IIR filters consisting of a parallel connection of two allpass filters. For a given magnitude response specification and a given number of pipeline stages in the feedback loop, our two-stage FRM approach requires fewer multipliers than the one-stage FRM approach if the number of pipeline stages is larger than four. In the FRM-based pipelined IIR filters with approximately linear phase, the bandedge shaping filters are a general IIR filter and its delay complementary filter. To design this kind of filters, we present a constrained optimization method that independently controls the passband phase error and magnitude error. A class of FRM-based IIR filters with IIR subfilters is also introduced in the thesis. In the proposed filter class, the bandedge shaping filters are a parallel connection of two allpass filters and the masking filters are approximately linear phase IIR filters composed of a parallel connection of a delay line and an allpass filter. By means of theoretical analysis and computer simulation, we demonstrate that the proposed class of FRM-based IIR filters has much better coefficient sensitivity and roundoff noise performances than conventional IIR filters.