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

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 banks with SOPOT coefficients

In this paper, a new family of multiplier-less two-channel low-delay 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

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

New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al. The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods. © 2004 IEEE.published_or_final_versio

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

In this paper, a new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filterbanks are parameterized by two functions (β(z) and α(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical β(z) and α(z) was considered by Phoong et al. with the delay parameter M chosen as 2N - 1. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase constraint is relaxed, the lengths of β(z) and α(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.published_or_final_versio

Efficient design of a class of multiplier-less perfect reconstruction two-channel filter banks and wavelets with prescribed output accuracy

The 11th IEEE Signal Processing Workshop on Statistical Signal Processing, Singapore, 6-8 August 2001This paper proposes a novel algorithm for the design and hardware reduction of a class of multiplier-less two-channel PR filter banks (FBs) using sum-of-powers-of-two (SOPOT) coefficient. It minimizes a more realistic hardware cost, such as adder cells, subject to a prescribe output accuracy taking into account of the rounding and overflow effects, instead of using just the SOPOT terms as in conventional method. Furthermore, by implementing the filters in the FBs using multiplier-block (MB), significant overall saving in hardware resources can be achieved. An effective random search algorithm is also proposed to solve the design problem, which is also applicable to PR IIR FBs with highly nonlinear objective functions.published_or_final_versio

On the design and implementation of a class of multiplier-less two-channel 1-D and 2-D nonseparable PR FIR filterbanks

This paper proposes a new design and implementation method for a class of multiplierless 2-channel 1D and 2D nonseparable perfect reconstruction (PR) filterbanks (FB). It is based on the structure proposed by S.M. Phoong et al. (see IEEE Trans. Sig. Proc., vol.43, p.649-64, 1995) and the use of multiplier blocks (MB). The latter technique allows one to further reduce the number of adders in implementing these multiplier-less FB by almost 50%, compared to the conventional method using sum of powers of two coefficients (SOPOT) alone. Furthermore, by generalizing the 1D to 2D transformation of Phoong et al., new 2D PR FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable FBs can be cascaded to realize new multiplierless PR directional FB for image processing and motion analysis. Design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio

The factorization of M-channel FIR and IIR cosine-modulated filter banks and their multiplier-less realizations using sopot coefficients

The 47th Midwest Symposium on Circuits and Systems Conference Proceedings, Salt Lake City, Utah, USA, 25-28 July 2004This paper proposes a new factorization for the M-channel perfect reconstruction (PR) IIR Cosine-Modulated filter banks (CMFB) proposed previously by the authors. This factorization, which is based on the lifting scheme, is also complete for the PR FIR CMFB as well as the general two-channel PR IIR filter banks if the determinant of the polyphase matrix is equal to constant multiplies of signal delays. It can be used to convert a numerically optimized nearly PR CMFB to a structurally PR system. Furthermore, the arithmetic complexity of the FB using this structure can be reduced asymptotically by a factor of two. When the forward and inverse transforms are implemented with the same set of SOPOT coefficients, a multiplier-less CMFB can be obtained. Its arithmetic complexity is further reduced and it becomes very attractive for VLSI implementation.published_or_final_versio