Paley‐Wiener‐Type theorems for the Clifford‐Fourier transform

Li, Shanshan; Leng, Jinsong; Fei, Minggang

doi:10.1002/mma.5707

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Lieb's Uncertainty Principle1

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2019

2024

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Cited by 12 publications

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“…In order to improve the above proposition, in the classical Fourier analysis, Lieb [24] estimated the L p -norm of the short-time Fourier transform using the Hausdorff-Young's inequality. However, as remarked in [23], it is not possible to extend this inequality in the Clifford setting since we cannot use the Riesz interpolation theorem.…”

Section: Lieb's Uncertainty Principlementioning

confidence: 99%

On the Clifford short-time Fourier transform and its properties

Martino¹

2021

Preprint

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In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier transform such as the orthogonality relation, the reconstruction property and the reproducing kernel formula. Moreover, we show the effects of modulating and translating the signal and the window function, respectively. Finally, we demonstrate the Lieb's uncertainty principle for the Clifford short-time Fourier transform.

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Section: Lieb's Uncertainty Principlementioning

confidence: 99%

On the Clifford short-time Fourier transform and its properties

Martino¹

2021

Preprint

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Spectrum‐Related Theories in the Framework of Quadratic Phase Fourier Transform

Varghese,

Kundu

2024

Math Methods in App Sciences

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In this article, new type of convolution and correlation theorems associated with quadratic phase Fourier transform (QPFT) are studied. Applications of that in multiplicative filter design, which may be useful in optics and signal processing to recover the signals, are also discussed. Besides that, the real Paley–Wiener (PW) and Boas theorem for QPFT are proved, which analyses the characteristics of the signals associated with QPFT in the domain.

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