Minimax Design of Two-Channel Nonuniform-Division Filterbanks Using IIR Allpass Filters

Abstract

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.

Design of IIR linear‐phase nonuniform‐division filter banks with signed powers‐of‐two coefficients

“…The performance for each continuous design of the IIR NDF banks is evaluated based on the filter coefficients provided by Lee and Yang [16]. …”

“…The desired magnitude responses for the low-pass and high-pass analysis filters H 0 (z) and H 1 (z) with pass-band bandwidths equal to p and ( − s ), respectively, are shown in Figure 2 [10], where p + s = 2 L 0 /L and L = L 0 + L 1 . H 0 (z) and H 1 (z) of Figure 1 are constructed as follows [16]:…”

“…The two-channel NDF bank system: (a) analysis system and (b) synthesis system (reproduced from Reference [16] (4) with orders N 1 and N 2 , respectively. Figure 3 shows the analysis portion of the proposed twochannel NDF bank structure.…”

“…Figure 3 shows the analysis portion of the proposed twochannel NDF bank structure. The corresponding frequency response of the NDF bank is given by [16] T (e…”

“…The parameters used for this design are listed as follows: L 0 = 2, L 1 = 3; 1 = 0.13, 2 = 0.13, 3 = 0.12; 1 = 1, 2 = 3, 3 = 100; and W = 10, d = 3, N A = 2. The significant design results, namely, PRE, NPSR, MVPR, MVGD and MVFBR designed by using the technique of Lee and Yang [16], GA and the proposed technique are shown in Table I A 2 (z) by using the proposed technique. The corresponding magnitude responses of the designed H i (e j ) are shown in Figure 4.…”