Gröbner bases and wavelet design

Jérôme Lebrun, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example, to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases.

Original languageEnglish (US)
Pages (from-to)227-259
Number of pages33
JournalJournal of Symbolic Computation
Volume37
Issue number2
DOIs
StatePublished - Feb 2004

Fingerprint

Wavelets
Filter
Spectral Factorization
Symbolic Methods
Multivariate Polynomials
Polynomial Systems
Factorization
System of equations
Signal Processing
Signal processing
Polynomials
Design

Keywords

  • Conjugate quadrature filters (CQFS)
  • Discrete wavelet transform (DWT)

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

Cite this

Gröbner bases and wavelet design. / Lebrun, Jérôme; Selesnick, Ivan.

In: Journal of Symbolic Computation, Vol. 37, No. 2, 02.2004, p. 227-259.

Research output: Contribution to journalArticle

Lebrun, Jérôme ; Selesnick, Ivan. / Gröbner bases and wavelet design. In: Journal of Symbolic Computation. 2004 ; Vol. 37, No. 2. pp. 227-259.
@article{f1b7b1ee5647465db619aa162a8beccc,
title = "Gr{\"o}bner bases and wavelet design",
abstract = "In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example, to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gr{\"o}bner algorithms offer an effective way to obtain solutions in some of these cases.",
keywords = "Conjugate quadrature filters (CQFS), Discrete wavelet transform (DWT)",
author = "J{\'e}r{\^o}me Lebrun and Ivan Selesnick",
year = "2004",
month = "2",
doi = "10.1016/j.jsc.2002.06.002",
language = "English (US)",
volume = "37",
pages = "227--259",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Gröbner bases and wavelet design

AU - Lebrun, Jérôme

AU - Selesnick, Ivan

PY - 2004/2

Y1 - 2004/2

N2 - In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example, to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases.

AB - In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example, to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases.

KW - Conjugate quadrature filters (CQFS)

KW - Discrete wavelet transform (DWT)

UR - http://www.scopus.com/inward/record.url?scp=1942445291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1942445291&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2002.06.002

DO - 10.1016/j.jsc.2002.06.002

M3 - Article

AN - SCOPUS:1942445291

VL - 37

SP - 227

EP - 259

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

IS - 2

ER -