Short-time special affine Fourier transform for quaternion-valued functions

The special affine Fourier transform is a promising tool for analyzing transient signals with more degrees of freedom via a chirp-like basis. In this article, our goal is to introduce a novel quaternion-valued short-time special affine Fourier transform in the context of two-dimensional quaternion-v...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022-04, Vol.116 (2), Article 66
Main Authors: Srivastava, H. M., Shah, Firdous A., Teali, Aajaz A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fourier transforms
Inequalities
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Quaternions
Theoretical
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Summary:The special affine Fourier transform is a promising tool for analyzing transient signals with more degrees of freedom via a chirp-like basis. In this article, our goal is to introduce a novel quaternion-valued short-time special affine Fourier transform in the context of two-dimensional quaternion-valued signals. In addition to studying all fundamental properties of the proposed transform, we also formulate some notable uncertainty inequalities including the Heisenberg-Weyl inequality, logarithmic inequality and local-type inequalities by employing the machinery of quaternionic Fourier transforms. Nevertheless, an illustrative example is presented to endorse the obtained results.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-022-01210-y