Rational Filter Wavelets

A new design algorithm for two-band orthonormal rational filter banks and orthonormal rational wavelets

In this paper, we present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (...

Wavelets And Filter Banks

Wavelet and short-time Fourier analysis is introduced in the context of frequency decompo-sitions. Wavelet type frequency decompositions are associated with lter banks, and using thisfact, lter bank theory is used to construct multiplicity M wavelet frames and tight frames. Theway in which lter banks lead to decomposition and recomposition of arbitrary separable Hilbertspaces is...

Wavelets by orthogonal rational kernels

Suppose f k g n k=0 is an orthonornal basis for the function space L n of polynomi-als or rational functions of degree n with prescribed poles. Suppose n = 2 s and set V s = L n. Then k n (z; w) = P n k=0 k (z) k (w), is a reproducing kernel for V s. For xed w, such reproducing kernels are known to be functions localized in the neighborhood of z = w. Moreover, by an appropriate choice of the pa...

Rational Wavelets on the Real Linea

Rational Wavelets on the Real Linea