2020/10/05 by Firdous A. Shah, Shah, Firdous A., Waseem Z. Lone +1
Computer Science · Earth and Planetary Sciences · Mathematics · #42C40. 43A70. 44A35. 42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2010.01972
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine wavelet transform and investigate the associated constant Q-property in the joint time-frequency domain. The preliminary analysis encompasses the derivation of the fundamental properties, orthogonality relation, inversion formula and range theorem. Finally, we extend the scope of the present study by introducing the notion of multi-resolution analysis associated with special affine wavelet transform and the construction of orthogonal special affine wavelets. We call it special affine multi-resolution analysis. The necessary and sufficient conditions pertaining to special affine Fourier domain under which the integer shifts of a chirp modulated functions form a Riesz basis or an orthonormal basis for a multi-resolution subspace is established.