Iacono, Mauro - ed. ; Kołodziej, Joanna - ed.
Title:Application of cubic box spline wavelets in the analysis of signal singularities
Subtitle: Group publication title: Subject and Keywords:cubic box splines ; wavelets ; dyadic wavelet transform ; singularity detection
Abstract:In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian) or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. ; The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters associated with cubic box wavelets that are applied in implementing the discrete dyadic wavelet transform are defined. The filters and the "algorithme ? trous" of the discrete dyadic wavelet transform are used in detecting signal singularities and in calculating the measures of signal singularities in the form of a Lipschitz exponent. The article presents examples illustrating the use of cubic box spline wavelets in the analysis of signal singularities.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 25, number 4 (2015) ; click here to follow the link
Language: License CC BY 4.0: Rights: