Journal ArticleDOI
Relationships between the radon-wigner and fractional fourier transforms
TLDR
The Radon-Wigner transform as mentioned in this paper is the squared modulus of the fractional Fourier transform, and it can be used to translate signal and image processing results between different signal representations.Abstract:
Two recently described transforms are shown to be related. The Radon–Wigner transform is the squared modulus of the fractional Fourier transform. This new theorem may serve to translate signal and image processing results between different signal representations. Some consequences regarding moments are presented, including a new fractional-Fourier-transform uncertainty relation. Implications for processing are suggested.read more
Citations
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Journal ArticleDOI
Digital computation of the fractional Fourier transform
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Journal ArticleDOI
Time--frequency feature representation using energy concentration: An overview of recent advances
TL;DR: Time-frequency domain signal processing using energy concentration as a feature is a very powerful tool and has been utilized in numerous applications and the expectation is that further research and applications of these algorithms will flourish in the near future.
Journal ArticleDOI
The discrete fractional Fourier transform
TL;DR: This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions, and is exactly unitary, index additive, and reduces to the D FT for unit order.
Book
Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale
TL;DR: In this article, the authors present a reconstruction of the Spectral Phase of a femtosecond light-matter system, including the phase shifts upon transmission-reflection, and four Photon Coherent Interaction.
Journal ArticleDOI
Fractional Fourier transform as a signal processing tool: An overview of recent developments
TL;DR: This paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT, which is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms.
References
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Journal ArticleDOI
The Fractional Order Fourier Transform and its Application to Quantum Mechanics
TL;DR: In this article, a generalized operational calculus is developed, paralleling the familiar one for the ordinary transform, which provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians.
Journal ArticleDOI
Image rotation, Wigner rotation, and the fractional Fourier transform
TL;DR: In this article, the degree p = 1 is assigned to the ordinary Fourier transform and the degree P = 1/2 to the fractional transform, where p is the degree of the optical fiber.
Book ChapterDOI
Parts I and II
E. P. Mazets,S. Golenetskii,V. N. Il'Inskii,V. N. Panov,R. Aptekar,Yu. A. Gur'yan,M. P. Proskura,I. A. Sokolov,Z. Ya. Sokolova,T. V. Kharitonova,A. V. Dyatchkov,N. G. Khavenson +11 more
TL;DR: In this article, the temporal structure, fluxes, energy spectra and coordinates of the sources of gamma-ray bursts detected in the KONUS experiment on Venera 11 andVenera 12 space probes were presented.
Journal ArticleDOI
Fractional Fourier transforms and their optical implementation. II
TL;DR: In this paper, the linear transform kernel for fractional Fourier transform is derived and the spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed.
Journal ArticleDOI
On Namias's fractional Fourier transforms
A. C. McBRIDE,F. H. Kerr +1 more
TL;DR: In this paper, it is stated que "for lever toute ambiguite, on montre qu'il est necessaire de modifier les operateurs fractionnaires de Namia On demontre des theoremes pour les operateur modifies and on developpe un calcul operationnel".