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Windowed Octonionic Fourier Transform

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Abstract

In this article, we introduce the concept of the windowed octonion Fourier transform (WOFT) by taking the octonion-valued function as the window function on the space of square integrable octonion-valued functions on \({\mathbb {R}}^3\). Some properties of the windowed octonion Fourier transform (WOFT) like left linearity, parity, specific shift, inversion, orthogonality and Hausdorff–Young inequality were also established. Towards the culmination of this paper, we establish the Pitt’s inequality and hence some uncertainty principle for the proposed transform. Some potential applications were also added to show the effectiveness of this paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Hazratbal, Srinagar, Jammu and Kashmir, 190006, India

    Younis Ahmad Bhat & Neyaz A. Sheikh

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  1. Younis Ahmad Bhat
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  2. Neyaz A. Sheikh
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Correspondence to Neyaz A. Sheikh.

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Bhat, Y.A., Sheikh, N.A. Windowed Octonionic Fourier Transform. Circuits Syst Signal Process 42, 2872–2896 (2023). https://doi.org/10.1007/s00034-022-02241-x

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