Journal ArticleDOI
A method for the discrete fractional Fourier transform computation
Min-Hung Yeh,Soo-Chang Pei +1 more
Reads0
Chats0
TLDR
A new method for the discrete fractional Fourier transform (DFRFT) computation is given and the DFRFT of any angle can be computed by a weighted summation of the D FRFTs with the special angles.Abstract:
A new method for the discrete fractional Fourier transform (DFRFT) computation is given in this paper. With the help of this method, the DFRFT of any angle can be computed by a weighted summation of the DFRFTs with the special angles.read more
Citations
More filters
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.
Journal ArticleDOI
Research progress of the fractional Fourier transform in signal processing
Ran Tao,Bing Deng,Yue Wang +2 more
TL;DR: The fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view and a course from the definition to the applications is provided, especially as a reference and an introduction for researchers and interested readers.
Journal ArticleDOI
Computation of the fractional Fourier transform
TL;DR: This note makes a critical comparison of some matlab programs for the digital computation of the fractional Fourier transform that are freely available and describes the own implementation that lters the best out of the existing ones.
Journal ArticleDOI
On the multiangle centered discrete fractional Fourier transform
J.G. Vargas-Rubio,Balu Santhanam +1 more
TL;DR: This letter defines a DFRFT based on a centered version of the DFT (CDFRFT) using eigenvectors derived from the Gru/spl uml/nbaum tridiagonal commutor that serve as excellent discrete approximations to the Hermite-Gauss functions.
Journal ArticleDOI
Recent developments in the theory of the fractional Fourier and linear canonical transforms
TL;DR: In recent years, there has been an enormous eort put in the denition and analysis of fractional or fractal operators as discussed by the authors, which are traditionally used in optics, mechanical engineering and signal processing.
References
More filters
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
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.
Book
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.
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.
Book
Fast Fourier transform and convolution algorithms
TL;DR: This book explains the development of the Fast Fourier Transform Algorithm and its applications in Number Theory and Polynomial Algebra, as well as some examples of its application in Quantization Effects.