Special affine wavelet transform and the corresponding Poisson summation formula

DOI10.1142/S0219691320500861zbMath1473.42044arXiv2006.05655OpenAlexW3107998786MaRDI QIDQ5010105

Azhar Y. Tantary, Aajaz A. Teali, Firdous Ahmad Shah

Publication date: 24 August 2021

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.05655

zbMATH Keywords

wavelet transformspecial affine Fourier transformgeneralized Poisson summation formulaspecial affine wavelet transformspecial affine Wigner distribution

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (5)

Free metaplectic wavelet transform in L2(ℝn) ⋮ Special affine multiresolution analysis and the construction of orthonormal wavelets in L²(ℝ) ⋮ Quadratic‐phase wavelet transform with applications to generalized differential equations ⋮ Linear canonical wavelet transform in quaternion domains ⋮ Short-time special affine Fourier transform for quaternion-valued functions

Cites Work

• Linear canonical transforms. Theory and applications
• The Poisson sum formulae associated with the fractional Fourier transform
• The generalization of the Poisson sum formula associated with the linear canonical transform
• Poisson summation formulae associated with the special affine Fourier transform and offset Hilbert transform
• A new fractional wavelet transform
• Windowed special affine Fourier transform
• Shift-invariant and sampling spaces associated with the special affine Fourier transform
• A generalized Poisson summation formula
• Wavelet Transforms and Their Applications
• Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation an operator approach
• Lecture Notes on Wavelet Transforms

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