title: On alternative wavelet reconstruction formula: a case study of approximate wavelets.
abstract: 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.
authors.affiliation: Mathematics and Mechanics Faculty, Saint Petersburg State University , Universitetsky prospekt 28, Peterhof , Saint Petersburg 198504, Russia ; Institute of Applied Mathematics and Mechanics, Saint Petersburg State Polytechnical University , Polytechnicheskay 29 , Saint Petersburg 195251, Russia.
authors.forename: Elena A
authors.identifier: 0000-0001-9054-7074
authors.initials: EA
authors.lastname: Lebedeva
authors.affiliation: Department of Theoretical Physics, Kursk State University , Radishcheva st. 33 , Kursk 305000, Russia.
authors.forename: Eugene B
authors.identifier: 0000-0001-7904-1881
authors.initials: EB
authors.lastname: Postnikov
keywords: Gaussian function; Hilbert transform; Morlet wavelet; admissibility condition; reconstruction formula; wavelet transform