Results 11 to 20 of about 97,044 (211)
Directional Short-Time Fourier Transform of Ultradistributions [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 We define and analyse the $k$-directional short-time Fourier transform and its synthesis operator over Gelfand Shilov spaces $\mathcal S^α_β(\mathbb R^n)$ and $\mathcal S^α_β(\mathbb R^{k+n})$ respectively, and their duals. Also, we investigate directional regular sets and their complements - directional wave fronts, for elements of $\mathcal S^{\prime
Sanja Atanasova +2 more
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The Short-Time Fourier Transform [PDF]
Signal Processing, 2001 We have seen that ideal time-frequency analysis faces a fundamental obstacle in the form of the uncertainty principle. Nevertheless, the example of the musical score indicates that a reasonable and useful form of time-frequency analysis should still be possible and realizable.
F.J Owens, M.S Murphy
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Uncertainty principles for the Fourier and the short-time Fourier transforms
Journal of Mathematical Physics, 2021 The aim of this paper is to establish a few uncertainty principles for the Fourier and the short-time Fourier transforms. In addition, we discuss an analog of the Donoho–Stark uncertainty principle and provide some estimates for the size of the essential support of the short-time Fourier transform.
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The Faber–Krahn inequality for the short-time Fourier transform
Inventiones mathematicae, 2022 AbstractIn this paper we solve an open problem concerning the characterization of those measurable sets $$\Omega \subset {\mathbb {R}}^{2d}$$ Ω ⊂ R 2
Nicola F., Tilli P.
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Planar Sampling Sets for the Short-Time Fourier Transform [PDF]
Constructive Approximation, 2020 This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class of windows in terms of a ...
Jaming, Philippe, Speckbacher, Michael
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On the Quaternionic Short-Time Fourier and Segal–Bargmann Transforms [PDF]
Mediterranean Journal of Mathematics, 2021 AbstractIn this paper, we study a special one-dimensional quaternion short-time 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.
Antonino De Martino, Kamal Diki
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Uncertainty principles for the short‐time Fourier transform on the lattice
Mathematische Nachrichten, 2023 AbstractIn this paper, we study a few versions of the uncertainty principle for the short‐time Fourier transform on the lattice . In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks‐type uncertainty principle, Heisenberg‐type uncertainty principle, and local uncertainty ...
Anirudha Poria, Aparajita Dasgupta
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On the polyanalytic short-time Fourier transform in the quaternionic setting
Communications on Pure and Applied Analysis, 2022 <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.
De Martino, A, Diki, K
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Zeros of the Wigner distribution and the short-time Fourier transform [PDF]
Revista Matemática Complutense, 2019 AbstractWe study the question under which conditions the zero set of a (cross-) Wigner distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions.
Karlheinz Gröchenig +2 more
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Short-time Fourier transform and superoscillations
Applied and Computational Harmonic Analysisto appear in Applied and Computational Harmonic ...
Daniel Alpay +3 more
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