<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>algorithme à trous</italic> 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.</p></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.

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Faculty of Management Białystok University of Technology, ul. Stefana Tarasiuka 2, 16-001 Kleosin, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities"}

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...

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Published Online: Dec 30, 2015

Page range: 927 - 941

Received: Jun 27, 2014

DOI: https://doi.org/10.1515/amcs-2015-0066

Keywords
cubic box splines, wavelets, dyadic wavelet transform, singularity detection

© 2015 Waldemar Rakowski, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Published Online: Dec 30, 2015

Page range: 927 - 941

Received: Jun 27, 2014

DOI: https://doi.org/10.1515/amcs-2015-0066

Keywordscubic box splines, wavelets, dyadic wavelet transform, singularity detection

© 2015 Waldemar Rakowski, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
cubic box splines, wavelets, dyadic wavelet transform, singularity detection