TY - JOUR

T1 - On alternative wavelet reconstruction formula: a case study of approximate wavelets

AU - Lebedeva, Elena A.

AU - Postnikov, Eugene B.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - wavelet transform

KW - Gaussian function

KW - Morlet wavelet

KW - reconstruction formula

KW - admissibility condition

KW - Hilbert transform

U2 - 10.1098/rsos.140124

DO - 10.1098/rsos.140124

M3 - Article

VL - 1

SP - 1

EP - 5

JO - Royal Society Open Science

JF - Royal Society Open Science

SN - 2054-5703

IS - 2

ER -