On the clifford short-time fourier transform and its properties

Martino, Antonino De

doi:10.1016/j.amc.2021.126812

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…The authors of [5] used the properties of STFT and 2D-complex Hermite polynomials to compute the spectrogram of white noise with Hermite windows. In the quaternionic and Clifford settings various counterparts of the short-time Fourier transform were developed recently in [19,20,21]. We refer to the book [30] and the references therein for further discussions on the STFT and related topics in time-frequency analysis.…”

Section: Introductionmentioning

confidence: 99%

Superoscillations and Fock spaces

Alpay,

Colombo,

Diki

et al. 2023

Journal of Mathematical Physics

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In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto a superposition of coherent states. Following this approach, the computations lead to a specific linear combination of the normalized reproducing kernels (coherent states) of the Fock space. As a consequence, we obtain two new integral Bargmann-type representations of superoscillating sequences. We also investigate some results relating superoscillation functions with Weyl operators and Fourier transform.

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Section: Introductionmentioning

confidence: 99%

Superoscillations and Fock spaces

Alpay,

Colombo,

Diki

et al. 2023

Journal of Mathematical Physics

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“…It is used in several applications such as the predictions of sound source position emanated by fault machine [38] and the interpretation of ultrasonic waveforms [35]. The short-time Fourier transform has been studied in quaternionic and Clifford settings in [11,22,23]. In particular in [23] we gave a definition of a quaternionic short-time Fourier transform (QSTFT) in dimension one for a Gaussian window.…”

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confidence: 99%

On the polyanalytic short-time Fourier transform in the quaternionic setting

Martino

Diki

2022

CPAA

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<p style='text-indent:20px;'>In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions. Indeed, we will use the notions of true and full slice polyanalytic Fock spaces and Segal-Bargmann transforms. We prove new properties of this QSTFT including a Moyal formula, a reconstruction formula and a Lieb's uncertainty principle. These results extend a recent paper of the authors which studies a QSTFT having a Gaussian function as a window.</p>

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“…Using the second one a quaternionic short-time Fourier transform in dimension 2 is studied in [5]. In the paper [16] the same transform is defined in a Clifford se ing for even dimension more than two. In this paper we introduce an extension of the short-time Fourier transform in a quaternionic se ing in dimension one.…”

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confidence: 99%

On the quaternionic short-time Fourier and Segal-Bargmann transforms

Martino¹,

Diki²

2020

Preprint

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A. In this paper, we study a special one dimensional quaternion shorttime Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal-Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb's uncertainty principle. We provide also the reproducing kernel associated to the Gabor space considered in this se ing.

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On the clifford short-time fourier transform and its properties

Cited by 7 publications

References 12 publications

Superoscillations and Fock spaces

Superoscillations and Fock spaces

On the polyanalytic short-time Fourier transform in the quaternionic setting

On the quaternionic short-time Fourier and Segal-Bargmann transforms

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