Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

“…In the literature are suggests the following extension method the series (Hadaś-Dyduch, 2014b, 2017Brislawn, 1996;Cohen, Daubechies, & Jawerth, 1993;Strang & Nguyen, 1996;Nason & Silverman, 1995):…”

Section: Extending Of the Time Seriesmentioning

confidence: 99%

Nonlinear Alleviation of Edge Effects in the Context of Minimizing Prediction Errors

Hadaś-Dyduch¹

2018

IJEF

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The aim of this article is to describe so-called "edge effects" in the context of wavelet analysis. The problem of "edge effects" is displayed in cases where the filter length is greater than 2. This is due to the fact that the calculation of the wavelet coefficients for the development of the last signal of finite elements, the filter -should theoretically move beyond the signal. The article describes different ways to solve this problem using an authored approach. One of the ways presented in the article is an innovative approach in terms of "edge effects". The author's proposal is based on the nonlinear function of the trend after the division of the series into smaller units. The results obtained show that in comparison with other methods, the author's method reduces errors. In this article, the Daubechies wavelet was used for the study. The Daubechies wavelets are a family of orthogonal wavelets, characterized by a maximum number of vanishing moments for a given support.

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“…Application of wavelet transforms to finite-length signals and, in particular, to images, requires an extension of signals beyond their boundaries [8]. The extension is even more important in our scheme since we implicitly assumed in our construction that the signals are defined on infinite intervals.…”

Section: Appendix I Implementation Of Recursive Filtersmentioning

confidence: 99%

“…The extension is even more important in our scheme since we implicitly assumed in our construction that the signals are defined on infinite intervals. When the filter banks are symmetric, the extension in the terminology of [8] is most efficient. It means that the signal , is symmetrically extended with the repetition of boundary samples through both ends of the interval.…”

Section: Appendix I Implementation Of Recursive Filtersmentioning

confidence: 99%