Evolutionary design of filter bank based on quaternions

This paper presents novel approach to the design of 4-channel filter bank composed of hypercomplex all-pass filters - a generalization of well known IIR all-passes to quaternion number system. This is uncommon alternative way of doing subband decomposition, but the design of such a system is difficult. Genetic algorithm was adopted to solve this hard numerical optimization task. The problem statement, the details of the evolutionary procedure and sample results are shown.

[1]  Michael de la Maza,et al.  Book review: Genetic Algorithms + Data Structures = Evolution Programs by Zbigniew Michalewicz (Springer-Verlag, 1992) , 1993 .

[2]  Shin‐Ichi Takahashi,et al.  Realization of two transfer functions with complex coefficients by a transfer function with hypercomplex coefficients , 1996 .

[3]  K. L. Ho,et al.  Multiplierless perfect reconstruction modulated filter banks with sum-of-powers-of-two coefficients , 2001, IEEE Signal Process. Lett..

[4]  Francesco Piazza,et al.  Improved power-of-two sharpening filter design by genetic algorithm , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[5]  Shing-Chow Chan,et al.  Multiplierless perfect reconstruction modulated filter banks with sum-of-powers-of-two coefficients , 2001, IEEE Signal Processing Letters.

[6]  S. Mitra,et al.  Digital all-pass networks , 1974 .

[7]  Hung-Ching Lu,et al.  Complex genetic algorithm approach for designing equiripple complex FIR digital filters with weighting function , 2000, Signal Process..

[8]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[9]  Masayuki Kawamata,et al.  GA-based design of multiplierless 2-D state-space digital filters with very small roundoff noise , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[10]  Sanjit K. Mitra,et al.  Design of doubly-complementary IIR digital filters, using a single complex allpass filter , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[11]  Holger Blume,et al.  FIR-filter design with spatial and frequency design constraints using evolution strategies , 1998, Signal Process..

[12]  H. Toyoshima Complex IIR digital filters composed of hypercomplex all-pass filters , 1995 .

[13]  A. S. Solodovnikov,et al.  Hypercomplex Numbers: An Elementary Introduction to Algebras , 1989 .

[14]  Stephen J. Sangwine Fourier transforms of colour images : the quaternion FFT , 1998 .