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Two-dimensional Fractional Stockwell Transform

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Abstract

In this paper, we introduce a new two-dimensional fractional Stockwell transform using the kernel of the coupled fractional Fourier transform. We establish that the two-dimensional fractional Stockwell transform satisfies all the expected properties including Parseval identity and inversion formula. We also characterize the range of the fractional Stockwell transform on \(\mathscr {L}^2(\mathbb {R}^2)\) and prove a convolution theorem of the transform. Finally, we prove the uncertainty principles for the coupled fractional Fourier transform as well as for the two-dimensional fractional Stockwell transform.

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Acknowledgements

The authors express their sincere thanks to the reviewers for their honest reviews, valuable comments and suggestions which highly improved the quality and clarity of this paper.

Funding

The work of Mr R. Kamalakkannan is supported by Junior Research Fellowship from Council of Scientific and Industrial Research-University Grants Commission (CSIR-UGC), India.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Tamil Nadu, Thiruvarur, 610005, India

    Ramanathan Kamalakkannan & Rajakumar Roopkumar

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  1. Ramanathan Kamalakkannan
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  2. Rajakumar Roopkumar
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Correspondence to Rajakumar Roopkumar.

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Kamalakkannan, R., Roopkumar, R. Two-dimensional Fractional Stockwell Transform. Circuits Syst Signal Process 41, 1735–1750 (2022). https://doi.org/10.1007/s00034-021-01858-8

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