Fractional Fourier transforms of hypercomplex signals [PDF]
Signal, Image and Video Processing, 2012 An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal.
De Bie, Hendrik, De Schepper, Nele
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Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann–Liouville Fractional Derivative [PDF]
Axioms, 2014 This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann ...
Ram K. Saxena +2 more
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Self Fourier functions and fractional Fourier transforms [PDF]
Optics Communications, 1993 The Fourier transform is perhaps the most important analytical tool in wave optics. Hence Fourier-related concepts are likely to have an important on optics. We will likely recall two novel concepts and then show how they are interrelated. A self-Fourier function (SFF) [1,2] is a function whose Fourier transform is identical to itself.
Mendlovic, D. +2 more
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Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms [PDF]
, 1994 Cataloged from PDF version of article.A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms.
Barshan, B. +3 more
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Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments
Sensors, 2021 Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years.
Chunpeng Wang +5 more
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Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures
Entropy, 2022 The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals.
Hari M. Srivastava +3 more
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Exact Relation Between Continuous and Discrete Linear Canonical Transforms [PDF]
, 2009 —Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs.
Figen S. Oktem, Haldun M. Ozaktas
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Improved discrete fractional Fourier transform [PDF]
Optics Letters, 1997 The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT's) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT.
S C, Pei, M H, Yeh
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Study on the Mainardi beam through the fractional Fourier transforms system [PDF]
Компьютерная оптика, 2018 In this paper, we introduced the Mainardi beam and indicated its attributes under the Fractional Fourier transform for power variations of Fractional Fourier transform.
Forouzan Habibi +2 more
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Sampling and series expansion theorems for fractional Fourier and other transforms [PDF]
, 2003 Cataloged from PDF version of article.We present muchbriefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms.
Candan, C., Ozaktas, H. M.
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