Marquardt optimization method to design two-channel quadrature mirror filter banks
Digital Signal Processing
Proceedings of the International Conference & Workshop on Emerging Trends in Technology
A study on construction of time-varying orthogonal wavelets
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
SEMCCO'11 Proceedings of the Second international conference on Swarm, Evolutionary, and Memetic Computing - Volume Part I
Journal of Signal Processing Systems
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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 (1995). 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.