A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. 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

Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications

M-Channel compactly supported biorthogonal cosine-modulated wavelet bases

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal Af-channel wavelet bases is equivalent to the design of a Af-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosinemodulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method for imposing the regularity on the CMFB's is also introduced, and several design examples are given. ©1998 IEEE.published_or_final_versio

Low-delay perfect reconstruction two-channel FIR/IIR filter banks and wavelet bases with SOPOT coefficients

IEEE International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey, 5-9 June 2000In this paper, a new family of two-channel low-delay filter banks and wavelet bases using the PR structure in [3] with SOPOT coefficients are proposed. In particular, the functions alpha(z) and beta(z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay filter banks with flexible lengths, delays, and regularity. Several design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

Designing two-channel causal stable IIR PR filter banks and wavelet bases by model order reduction and constrained optimization

In this paper, two methods for designing two-channel causal stable IIR PR filter banks are introduced. The first method makes use of model reduction and constrained optimization to obtain a causal stable IIR filter bank from the structural PR FIR filter bank proposed in [2]. It yields better frequency characteristics than the original FIR filter bank and avoids the dump at π/2 when allpass filters are used. Using the 1-D to 2-D transformation proposed in [2], two dimensional PR IIR filter bank can readily be obtained from these prototypes. The second method is based on constrained optimization technique using the general PR condition. Using this technique, filter banks with low system delay and flexible frequency characteristics can be designed. The technique can also be modified to design causal stable IIR dyadic wavelet bases with added regularity conditions. A number of design examples are used to demonstrate the usefulness of the proposed design methods.published_or_final_versio

Low-delay perfect reconstruction two-channel FIR/IIR filter banks and wavelet bases with SOPOT coefficients

IEEE International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey, 5-9 June 2000In this paper, a new family of two-channel low-delay filter banks and wavelet bases using the PR structure in [3] with SOPOT coefficients are proposed. In particular, the functions alpha(z) and beta(z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay filter banks with flexible lengths, delays, and regularity. Several design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

Multiplier-less low-delay FIR and IIR wavelet filter bank with SOPOT coefficients

In this paper, a new family of multiplier-less two-channel lowdelay wavelet filter banks using the PR structure in [3] and the SOPOT(sum-of-powers-of-two) representation is proposed. In particular, the functions α (z) and β (z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay wavelet bases with flexible length, delay, and number of zero at π (or 0) in their analysis filters. Several design examples are given to demonstrate the usefulness of the proposed method.postprin