6533b7defe1ef96bd12767d8

RESEARCH PRODUCT

Biorthogonal Wavelet Transforms

Pekka NeittaanmäkiValery A. ZheludevAmir Averbuch

subject

Discrete wavelet transformPolynomialSpline (mathematics)Pure mathematicsWaveletBiorthogonal systemFilter bankBiorthogonal waveletMathematicsWavelet packet decomposition

description

Wavelets in the polynomial and discrete spline spaces were introduced in Chaps. 8 and 10, respectively. In both cases, the wavelets’ design and implementation of the transforms were associated with perfect reconstruction (PR) filter banks. In this chapter, those associations are discussed in more detail. Biorthogonal wavelet bases generated by PR filter banks are investigated and a few examples of compactly supported biorthogonal wavelets are presented. Conditions for filters to restore and annihilate sampled polynomials are established (discrete vanishing moment property). In a sense, the material of this chapter is introductory to Chap. 12, where splines are used as a source for (non-spline) wavelets’ design.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-94-017-8926-4_15