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.
- Conjugate quadrature filters (CQFS)
- Discrete wavelet transform (DWT)
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics