Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter we give an overview of a method recently developed for designing wavelet filter banks via the Quillen-Suslin Theorem for Laurent polynomials. In this method, the Quillen-Suslin Theorem is used to transform vectors with Laurent polynomial entries to other vectors with Laurent polynomial entries so that the matrix analysis tools that were not readily available for the vectors before the transformation can now be employed. As a result, a powerful and general method for designing non-redundant wavelet filter banks is obtained. In particular, the vanishing moments of the resulting wavelet filter banks can be controlled in a very simple way, which is especially advantageous compared to other existing methods for the multi-dimensional cases.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages303-313
Number of pages11
Edition9783319547107
DOIs
Publication statusPublished - 2017 Jan 1

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319547107
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Laurent Polynomials
Filter Banks
Filter banks
Wavelets
Polynomials
Theorem
Vanishing Moments
Matrix Analysis
Transform
Design

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Hur, Y. (2017). Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. In Applied and Numerical Harmonic Analysis (9783319547107 ed., pp. 303-313). (Applied and Numerical Harmonic Analysis; No. 9783319547107). Springer International Publishing. https://doi.org/10.1007/978-3-319-54711-4_12
Hur, Youngmi. / Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. Applied and Numerical Harmonic Analysis. 9783319547107. ed. Springer International Publishing, 2017. pp. 303-313 (Applied and Numerical Harmonic Analysis; 9783319547107).
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Hur, Y 2017, Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. in Applied and Numerical Harmonic Analysis. 9783319547107 edn, Applied and Numerical Harmonic Analysis, no. 9783319547107, Springer International Publishing, pp. 303-313. https://doi.org/10.1007/978-3-319-54711-4_12

Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. / Hur, Youngmi.

Applied and Numerical Harmonic Analysis. 9783319547107. ed. Springer International Publishing, 2017. p. 303-313 (Applied and Numerical Harmonic Analysis; No. 9783319547107).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Hur Y. Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. In Applied and Numerical Harmonic Analysis. 9783319547107 ed. Springer International Publishing. 2017. p. 303-313. (Applied and Numerical Harmonic Analysis; 9783319547107). https://doi.org/10.1007/978-3-319-54711-4_12