Ternary wavelets and their applications to signal compression

Ghulam Mustafa; Falai Chen; Zhangjin Huang

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 233-240
  • ISSN: 1641-876X

Abstract

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We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.

How to cite

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Mustafa, Ghulam, Chen, Falai, and Huang, Zhangjin. "Ternary wavelets and their applications to signal compression." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 233-240. <http://eudml.org/doc/207694>.

@article{Mustafa2004,
abstract = {We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.},
author = {Mustafa, Ghulam, Chen, Falai, Huang, Zhangjin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {multiresolution; signal compression; wavelets; subdivision; multiresolution analysis; ternary wavelets},
language = {eng},
number = {2},
pages = {233-240},
title = {Ternary wavelets and their applications to signal compression},
url = {http://eudml.org/doc/207694},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Mustafa, Ghulam
AU - Chen, Falai
AU - Huang, Zhangjin
TI - Ternary wavelets and their applications to signal compression
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 233
EP - 240
AB - We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.
LA - eng
KW - multiresolution; signal compression; wavelets; subdivision; multiresolution analysis; ternary wavelets
UR - http://eudml.org/doc/207694
ER -

References

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