Interpolating Filters with Prescribed Zeros and Their Refinable Functions

Analysis and Construction of Multivariate Interpolating Refinable Function Vectors

In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and ana...

Generalized interpolating refinable function vectors

Interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory, signal processing, computer graphics, and numerical algorithms. In this paper, we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating d-refinable function vectors with any multiplicity r and dilation factor d. Mor...

Interpolating Refinable Functions and Wavelets for General Scaling Matrices

Construction of biorthogonal wavelets from pseudo-splines

Pseudo-splines constitute a new class of refinable functions with B-splines, interpolatory refinable functions and refinable functions with orthonormal shifts as special examples. Pseudo-splines were first introduced by Daubechies, Han, Ron and Shen in [Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14(1) (2003), 1–46] and Selenick in [Smooth wavelet tight fra...

Synthesis of Generalized Chebyshev Lossy Bandstop Filters with Non-Paraconjugate Transmission Zeros

A systematic procedure is presented for synthesis of generalized Chebyshev lossy bandstop filters with non-paraconjugate transmission zeros. From a lossy scattering parameters with the prescribed reflection zeros, the transformation formulas from the scattering matrix to the admittance matrix are obtained by reconstructing the non-paraconjugate transmission zeros as paraconjugate ones. The cano...