Geodesic
Two-sided quaternion wave-packet transform and the quantitative uncertainty principles
Filomat, Tome 36 (2022) no. 2, p. 449

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DOI

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
DOI : 10.2298/FIL2202449S
Classification : 42C40, 42B10, 65M70, 44A05
Keywords: Quaternion wave-packet transform, Quaternion valued function, Quaternion wavelet, Uncertainty principle, Two-sided quaternion Fourier transform 
Firdous A Shah; Aajaz A Teali. Two-sided quaternion wave-packet transform and the quantitative uncertainty principles. Filomat, Tome 36 (2022) no. 2, p. 449 . doi: 10.2298/FIL2202449S
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     doi = {10.2298/FIL2202449S},
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