Journal ArticleDOI
Some important fractional transformations for signal processing
TLDR
This paper suggests a generalization of the Hartley transformation based on the fractional Fourier transform, coined it “fractional Hartley transform (FHT)” and additional useful transformations used for signal processing are discussed.About:
This article is published in Optics Communications.The article was published on 1996-04-01. It has received 80 citations till now. The article focuses on the topics: Hartley transform & Discrete Hartley transform.read more
Citations
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Journal ArticleDOI
Fractional Order Systems in Industrial Automation—A Survey
TL;DR: This paper describes linear and nonlinear cases with necessary stability and performance considerations for the benefit of a practicing engineer exploiting informatics in industry.
Journal ArticleDOI
The discrete fractional cosine and sine transforms
Soo-Chang Pei,Min-Hung Yeh +1 more
TL;DR: The computations of DFRFT for even or odd signals can be planted into the half-size DFRCT and DFRST calculations, which will reduce the computational load of the DFR FT by about one half.
Book ChapterDOI
Introduction to the Fractional Fourier Transform and Its Applications
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors is a generalization of the ordinary FFT with an order parameter a, and it is used to interpolate between a function f(u) and its FFT F(μ).
Journal Article
Fractional Fourier transform: A novel tool for signal processing
Rajiv Saxena,Kulbir Singh +1 more
TL;DR: In this article, the authors discuss discrete fractional Fourier transform (DFRFT), time-frequency distributions related to FRFT, optimal filter and beamformer in FRFT domain, filtering using window functions and other fractional transforms along with simulation results.
Journal ArticleDOI
Novel image encryption algorithm based on multiple-parameter discrete fractional random transform
TL;DR: The computer simulation results show that the proposed encryption algorithm is sensitive to the multiple keys, and that it has considerable robustness, noise immunity and security.
References
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Journal ArticleDOI
The fractional Fourier transform and time-frequency representations
TL;DR: The authors briefly introduce the functional Fourier transform and a number of its properties and present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time- frequencies such as the Wigner distribution, the ambiguity function, the short-time Fouriertransform and the spectrogram.
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.
Journal ArticleDOI
Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
TL;DR: Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains.
Journal ArticleDOI
Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.
TL;DR: It is shown that both definitions of a fractional Fourier transform are equivalent, and an important result is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium.