Abstract
In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion-valued signals, and we give several important properties such as the Plancherel formula and inversion formula. Finally, we establish the Heisenberg uncertainty principles for the GQFT.
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El Kassimi, M., Fahlaoui, S. (2020). The Two-Sided Gabor Quaternionic Fourier Transform and Uncertainty Principles. In: Dos Santos, S., Maslouhi, M., Okoudjou, K. (eds) Recent Advances in Mathematics and Technology. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-35202-8_1
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DOI: https://doi.org/10.1007/978-3-030-35202-8_1
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