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SIAM journal on scientific computing, ISSN 1064-8275, 2007, Volume 30, Issue 2, pp. 764 - 784
The Fourier transform of a continuous function, evaluated at frequencies expressed in polar coordinates, is an important conceptual tool for understanding physical continuum phenomena... 
Concentric-squares grid | Unequally spaced FFT | Linogram | Polar Fourier transform | Pseudopolar Fourier transform | Fractional Fourier transform | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
IMA journal of applied mathematics, ISSN 0272-4960, 2018, Volume 83, Issue 6, pp. 908 - 916
Based on the definition of the continuous Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the continuous fractional Fourier... 
Fourier transform | Discrete fractional Fourier transform | Vandermonde matrices | Confluent Vandermonde matrices | Discrete Fourier transform | Fractional Fourier transform | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Circuits, systems, and signal processing, ISSN 1531-5878, 09/2018, Volume 38, Issue 4, pp. 1751 - 1774
Journal Article
Wireless personal communications, ISSN 0929-6212, 1/2017, Volume 92, Issue 2, pp. 623 - 637
Journal Article
IEEE transactions on signal processing, ISSN 1053-587X, 02/2014, Volume 62, Issue 4, pp. 939 - 953
Journal Article
Signal processing, ISSN 0165-1684, 05/2014, Volume 98, pp. 158 - 165
The fractional Fourier transform (FRFT), a generalization of the Fourier transform, has proven to be a powerful tool in optics and signal processing... 
Sampling theorem | Riesz bases | Function spaces | Truncation error | Fractional Fourier transform | Engineering, Electrical & Electronic | Engineering | Technology | Science & Technology | Electrical engineering | Analysis | Fourier transforms | Theorems | Function space | Signal processing | Derivation | Band theory | Truncation errors | Sampling
Journal Article
Signal, image and video processing, ISSN 1863-1703, 2/2018, Volume 12, Issue 2, pp. 379 - 383
Journal Article
Optical Engineering, ISSN 0091-3286, 05/2003, Volume 42, Issue 6, pp. 1583 - 1588
We implement a fully phase encryption system, using fractional Fourier transform to encrypt and decrypt a 2-D phase image obtained from an amplitude image... 
photorefractive crystal | phase conjugation | data security | fractional Fourier transform | optical encryption | phase contrast | decryption | Fractional fourier transform | Data security | Phase contrast | Photorefractive crystal | Decryption | Optical encryption | Phase conjugation | Optics | Physical Sciences | Science & Technology
Journal Article
Optical Engineering, ISSN 0091-3286, 05/2011, Volume 50, Issue 6, pp. 068201 - 068201
In this paper, an optical color image encryption/decryption technology based on joint fractional Fourier transform correlator and double random phase encoding (DRPE) is developed... 
color image | optical security | encryption | joint fractional Fourier transformcorrelator | Optics | Physical Sciences | Science & Technology | Correlation | Fourier transforms | Phase transformations | Color | Images | Parallel processing | Encryption | Security
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 08/2014, Volume 266, pp. 73 - 86
In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in a given range of the frequency... 
Fourier transform | Continuous Euler transform | Fractional FFT | Error control | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematics - Numerical Analysis
Journal Article
Applied and computational harmonic analysis, ISSN 1063-5203, 2004, Volume 16, Issue 3, pp. 182 - 202
In this paper we make a critical comparison of some Matlab programs for the digital computation of the fractional Fourier transform that are freely available and we describe our own implementation... 
Fractional Fourier transform | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Fourier transforms | Algorithms
Journal Article