Multirate signal processing on finite fields

The paper addresses the problem of multirate signal processing over arbitrary fields. Studies of multirate systems and filter banks have proceeded in parallel, and a wealth of results are available in literature. The authors concentrate their attention on cyclic systems. These structures are ideally suited to generalising the concepts to finite fields. The perfect reconstruction property for quadrature mirror filter banks is obtained. It is shown how the cyclic wavelet transform (CWT) can be derived from such systems; the relationships between cyclic filter banks and CWTs are explored in detail. The results obtained are potentially very well suited for speech and image encoding, as well as for fast algorithms in signal processing.

[1]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[2]  Richard E. Blahut,et al.  Fast Algorithms for Digital Signal Processing , 1985 .

[3]  Jan P. Allebach,et al.  Multidimensional Signal Processing , 1997 .

[4]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[5]  John W. Woods,et al.  Subband coding of images , 1986, IEEE Trans. Acoust. Speech Signal Process..

[6]  H. Vincent Poor,et al.  Cyclic wavelet transforms for arbitrary finite data lengths , 2000, Signal Process..

[7]  Nikil Jayant,et al.  Signal Compression: Technology Targets and Research Directions , 1992, IEEE J. Sel. Areas Commun..

[8]  I. Herstein,et al.  Topics in algebra , 1964 .

[9]  R. Blahut.  Theory and practice of error control codes , 1983 .

[10]  H. Vincent Poor,et al.  Multiband cyclic wavelet transforms , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[11]  Jae S. Lim,et al.  Advanced topics in signal processing , 1987 .

[12]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[13]  P. P. Vaidyanathan,et al.  Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial , 1990, Proc. IEEE.

[14]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[15]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[16]  P. Vaidyanathan.  Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques , 1987, IEEE ASSP Magazine.

[17]  James D. Johnston,et al.  Transform coding of audio signals using perceptual noise criteria , 1988, IEEE J. Sel. Areas Commun..

[18]  Richard E. Blahut.  Algebraic Methods for Signal Processing and Communications Coding , 1991 .

[19]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[20]  L. Rabiner,et al.  Multirate digital signal processing: Prentice-Hall, Inc. Englewood Cliffs, New Jersey 07362, 1983, 411 pp., ISBN 0-13-605162-6 , 1983 .

[21]  Sandip Sarkar.  Cyclic wavelet transforms and error control coding , 1996 .

[22]  Robert L. Grossman,et al.  Wavelet transforms associated with finite cyclic groups , 1993, IEEE Trans. Inf. Theory.

[23]  Richard E. Blahut.  Fast Algorithms for Signal Processing and Error Control , 1985 .

[24]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..