Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties [PDF]
arXiv, 2018 In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also ...
arxiv
Fourier transform and middle convolution for irregular D-modules [PDF]
arXiv, 2008 S.Block and H.Esnault constructed the local Fourier transform for D-modules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the local version of Katz's middle convolution.
arxiv
Calculation of local Fourier transforms for formal connections [PDF]
arXiv, 2007 We calculate the local Fourier transforms for formal connections. In particular, we verify an analogous conjecture suggested in Laumon's paper: "Transformation de Fourier, constantes d'equations fonctionnelles et conjecture de Weil, 2.6.3".
arxiv
A New Viewpoint to the Discrete Approximation: Discrete Yang-Fourier Transforms of Discrete-time Fractal Signal [PDF]
arXiv, 2011 It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.
arxiv
Discrete and Fast Fourier Transform Made Clear [PDF]
arXiv, 2019 Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means of elementary linear algebra.
arxiv
Growth and integrability of Fourier transforms on Euclidean space [PDF]
arXiv, 2013 A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of $L^{p}-$multipliers, a rather general inequality controlling the size of Fourier transforms for large and small argument is proved. As consequences, quantitative Riemann-
arxiv
Quadratic discrete Fourier transform and mutually unbiased bases [PDF]
Quadratic discrete Fourier transform and mutually unbiased bases,
G. Nikolic (Ed.) (2010) 103-138, 2010 The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the ...
arxiv
Fonctions de Mittag-Leffler et processus de Lévy stables sans saut négatif [PDF]
arXiv, 2009 It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity in law between suprema of completely asymmetric Levy a-stable processes.
arxiv
Standard Poster Abstracts for the 17th Asia Pacific Heart Rhythm Society (APHRS) Scientific Sessions
Journal of Arrhythmia, Volume 41, Issue 2, April 2025.
wiley +1 more source
A mathematical survey on Fourier type integral transform and their offshoots: windowed Fourier transform, wavelet transform and Stockwell transform [PDF]
arXivThis comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT), quadratic phase Fourier transform (QPFT), and their associated offshoots: windowed Fourier transform, wavelet ...
arxiv