Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

Abstract

Abslraci --It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (foi example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H('z) (for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined.

Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants

“…Example 4: A simple two-band example of an aliasfree system with lossless P ( z ) can be found in [28] and [30] where the analysis and synthesis filters are as in (20a) with the additional stipulation that the polyphase compo-…”

Two-Channel Quadrature Mirror Filter Bank: An Overview

“…Several methods [52][53][54][55][56][57] have been developed using IIR filters to design NPR QMF bank. In these design techniques ALD and AMD eliminated completely, and PHD is minimized.…”

A New Class of Two-Channel Biorthogonal Filter Banks and Wavelet Bases.

“…The earliest good designs for the IIR case were such that the analysis bank was paraunitary and the polyphase components of H o ( z ) and H I ( % ) were allpass (see [7], and p. 201 of [2] Some of the results in this paper were reported in the earlier conference papers [20]- [22]. For the 1-D case [20], both of the linear phase FIR and causal stable IIR solutions for PR filter banks similar to those proposed in this paper were given.…”

“…In this case, Ho(z) is a sum of a delay and an allpass function. See (7). It is an IIR halfband filter and has been studied by some researchers [27], [28].…”

“…The mapping preserves the following: i) perfect reconstruction ii) stability in the IIR case iii) linear phase in the FIR case iv) zeros at aliasing frequency v) frequency characteristic of the filters. [7]. If for all input ~( n ) , the output of the system 2(n) = C X (~ -no) for some nonzero constant c and integer no, the system is called a perfect reconstruction (PR) system.…”