# 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 language English (US) 227-259 33 Journal of Symbolic Computation 37 2 https://doi.org/10.1016/j.jsc.2002.06.002 Published - Feb 2004

### Fingerprint

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

### Keywords

• 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.
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