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The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
This phenomena is related to the invariant cycles under the transformation We also give a characterization of all low-pass filters for MSF wavelets.
      
The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
We also give a characterization of all low-pass filters for MSF wavelets.
      
Unitary mappings between multiresolution analyses of L2 (R) and a parametrization of low-pass filters
      
These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L2([-π, π)), which we characterize.
      
We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures.
      
This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices.
      
The characterization of low pass filters and some basic properties of wavelets, scaling functions and related concepts
      
Only certain smooth classes of the low pass filters that are determined by these scaling functions, however, appear to be characterized in the literature (see Chapter 7 of [3] for an account of these matters).
      
In this paper we present a complete characterization of all these filters.
      
This somewhat technical result does provide a method for simple constructions of low pass filters whose only smoothness assumption is a Holder condition at the origin.
      
An Inhomogeneous Uncertainty Principle for Digital Low-Pass Filters
      
This article introduces an inhomogeneous uncertainty principle for digital lowpass filters.
      
We derive a sharp lower bound for this product in the class of filters with so-called finite effective length and show the absence of minimizers.
      
When the class of filters is restricted to a given maximal length, we show the existence of an uncertainty minimizer.
      
The uncertainty product of such minimizing filters approaches the unrestricted infimum as the filter length increases.
      
We examine the asymptotics and explicitly construct a sequence of finite-length filters with the same asymptotics as the sequence of finite-length minimizers.
      
Moreover, it will be shown that such decompositions give rise to stable filtering schemes with finitely supported filters, reminiscent of those studied by Kovacevic and Vetterli.
      
The design problem of biorthogonal linear-phase scaling filters and wavelet filters as a quadratic programming problem with the linear constraints is formulated.
      
 

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