On alternative wavelet reconstruction formula: a case study of approximate wavelets

• Main Authors: Elena A. Lebedeva, Eugene B. Postnikov
• Format: Article
• Language: English
• Published: The Royal Society 2014-01-01
• Series: Royal Society Open Science
• Subjects: wavelet transform; gaussian function; morlet wavelet; reconstruction formula; admissibility condition; hilbert transform
• Online Access: https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140124

The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.