The system of translates and the special affine Fourier transform
Md Hasan Ali Biswas, Frank Filbir, Radha Ramakrishnan
TL;DR
This paper introduces the translation operator for the special affine Fourier transform (SAFT), establishes key harmonic analysis theorems in this context, and explores shift-invariant spaces and sampling related to SAFT.
Contribution
It develops the harmonic analysis framework for SAFT, including translation operators, classical theorems, and sampling theory, which are new contributions.
Findings
Defined the translation operator $T^A$ for SAFT
Established analogues of classical harmonic analysis theorems for SAFT
Studied shift-invariant spaces and sampling problems in the SAFT context
Abstract
The translation operator associated with the special affine Fourier transform (SAFT) is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and Bernstein type inequality in the context of the SAFT are established. The shift invariant space associated with the special affine Fourier transform is introduced and studied along with sampling problems.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Image and Signal Denoising Methods · Seismic Imaging and Inversion Techniques