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Paper details
Number 4 - December 2015
Volume 25 - 2015
Application of cubic box spline wavelets in the analysis of signal singularities
Waldemar Rakowski
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 à 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.
Keywords
cubic box splines, wavelets, dyadic wavelet transform, singularity detection