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A certain family of fractional wavelet transformations
Author(s) -
Srivastava Hari M.,
Khatterwani Komal,
Upadhyay S. K.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5570
Subject(s) - mathematics , wavelet , harmonic wavelet transform , wavelet transform , orthonormal basis , discrete wavelet transform , fractional fourier transform , fourier transform , mathematical analysis , stationary wavelet transform , fourier analysis , computer science , artificial intelligence , physics , quantum mechanics
In the present paper, a fractional wavelet transform of real order α is introduced, and various useful properties and results are derived for it. These include (for example) Perseval's formula and inversion formula for the fractional wavelet transform. Multiresolution analysis and orthonormal fractional wavelets associated with the fractional wavelet transform are studied systematically. Fractional Fourier transforms of the Mexican hat wavelet for different values of the order α are compared with the classical Fourier transform graphically, and various remarkable observations are presented. A comparative study of the various results, which we have presented in this paper, is also represented graphically.