Open AccessTwo-sided quaternion wave-packet transform and the quantitative uncertainty principles
Author(s) -
Firdous A. Shah,
Aajaz A. Teali
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202449s
Subject(s) - mathematics , quaternion , fourier transform , orthogonality , harmonic wavelet transform , parseval's theorem , relation (database) , inversion (geology) , uncertainty principle , logarithm , range (aeronautics) , algebra over a field , fractional fourier transform , algorithm , wavelet , wavelet transform , mathematical analysis , wavelet packet decomposition , pure mathematics , fourier analysis , computer science , geometry , artificial intelligence , quantum mechanics , materials science , structural basin , database , composite material , quantum , biology , paleontology , physics
In this article, we introduce the notion of two-sided quaternion wave-packet transform which inherits the advantages of both the quaternion windowed Fourier and wavelet transforms with some additional promising features. The preliminary analysis encompasses the derivation of fundamental properties including, orthogonality relation, energy preserving relation, inversion formula and the range theorem by utilizing the machinery of two-sided quaternion Fourier transforms. Besides, we also derive the Heisenberg?s and logarithmic uncertainty principles for the proposed transform. We culminate our investigation by presenting some illustrative examples.