Stable Filtering Schemes with Rational Dilations
نویسنده
چکیده
The relationship between multiresolution analysis and filtering schemes is a well-known facet of wavelet theory. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. This work seeks to establish a means for the construction of stable filtering schemes with rational dilations through the theory of shift-invariant spaces. In particular, principal shift-invariant spaces will be shown to offer frame wavelet decompositions for rational dilations even when the associated scaling function is not refinable. Moreover, it will be shown that such decompositions give rise to stable filtering schemes with finitely supported filters, reminiscent of those studied by Kovačević and Vetterli.
منابع مشابه
Generalized Stable Multivariate Distribution and Anisotropic Dilations
After having closely re-examined the notion of a Lévy’s stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct ...
متن کاملThe wavelet dimension function for real dilations and dilations admitting non-MSF wavelets
The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...
متن کاملAn Accurate Operator Splitting Scheme for Nonlinear Diffusion Filtering
nonlinear diffusion filtering, operatorsplitting schemes, bilateral filtering Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [15]. AOS schemes are efficient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diffusion filtering may require better accuracy at the expense of a rel...
متن کاملAPPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES
We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.
متن کاملSpeech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering
This paper presents new adaptive filtering techniques used in speech enhancement system. Adaptive filtering schemes are subjected to different trade-offs regarding their steady-state misadjustment, speed of convergence, and tracking performance. Fractional Least-Mean-Square (FLMS) is a new adaptive algorithm which has better performance than the conventional LMS algorithm. Normalization of LMS ...
متن کامل