Half-band (HB) filters are of great importance and are often used in multirate digital signal processing systems, filter banks and wavelets. In this paper, a new closed-form expression for the transfer function of the maximally flat (MF) infinite-impulse response (IIR) HB filters is presented. The filter coefficients are directly obtained by solving a linear system of Vandermonde equations that...

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach has the following attractive features: It achieves O(N) complexity per scale, the filter coefficients can be analytically obtained by a simple integration, and the algorithm is faster than a least squares approach with negligible loss in accuracy. Our method is to use P wavelets per octave ...

The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provi...

Computational algorithms have been developed for generating min-length max-flat FIR filter coefficients for orthogonal and biorthogonal wavelets with varying degrees of asymmetry or symmetry. These algorithms are based on spectral factorization of the Daubechies polynomial with a combinatorial search of root sets selected by a desired optimization criterion. Daubechies filter families were syst...

This paper discusses a method of regularity imposition onto biorthogonal linear-phase -band filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and synthesis filterbanks having up to two degrees of regularity. Necessary and sufficient conditions for regu...

In 2006 Guo, Labate, Lim, Weiss, and Wilson introduced the theory of MRA composite dilation wavelets. We continue their work by studying the filter properties of such wavelets and present several important examples.

In this paper, we compare different adaptation criterions of the proposed two dimensional wavelet filter bank with a variable number of zero moments. Twodimensional generalization of the previously reported 1D algorithm is based on nonseparable quincunx scheme. 2-D filters were designed directly, rather then obtained from 1-D filters using pyramid scheme. Filter banks with more zero moments are...

Abstract: In the application with multiple data streams, the correlation between data streams is very significant. The main contributions of this paper included: (1) Introduces the concept of total ordering with filter and compression by wavelets to describe streams. (2) Proposes the equivalence model to evaluate correlations between streams, including three theorems about the equivalence betwe...

The computation of wavelet coefficients of a function typically requires the computation of a large number of integrals. These integrals represent the inner product of that function with a wavelet function on different scales, or with the corresponding scaling function on a fine scale. We develop quadrature rules for those integrals that converge fast for piecewise smooth and singular functions...

The Laguerre method for the numerical inversion of Laplace transforms is a well known approach to the approximation of probability density functions (PDFs) and cumulative distribution functions (CDFs) of first passage times in Markov chains. Results are presented that relate the Laguerre generating functions and Laguerre coefficients of a PDF with those of the corresponding complementary CDF. T...