Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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TL;DR: Under certain conditions it is shown that discrete-time sequences carry redundant information which then allow for the detection and correction of errors.
Abstract: The relationship between the discrete Fourier transform and error-control codes is examined. Under certain conditions we show that discrete-time sequences carry redundant information which then allow for the detection and correction of errors. An application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described.
185 citations
TL;DR: A new image encryption algorithm based on a generalized fractional Fourier transform, to which it is referred as a multifractional Fouriers transform, is proposed.
Abstract: We propose a new image encryption algorithm based on a generalized fractional Fourier transform, to which we refer as a multifractional Fourier transform. We encrypt the input image simply by performing the multifractional Fourier transform with two keys. Numerical simulation results are given to verify the algorithm, and an optical implementation setup is also suggested.
182 citations
TL;DR: In this article, the authors present the essential ideas underlying the fast Fourier transform (NUFFT) algorithm in simple terms, and illustrate its utility with application to problems in magnetic resonance imaging and heat flow.
180 citations
TL;DR: This letter shows that the fractional Fourier transform is nothing more than a variation of the standard Fouriertransform and, as such, many of its properties can be deduced from those of the Fourier Transform by a simple change of variable.
Abstract: In recent years, the fractional Fourier transform has been the focus of many research papers. In this letter, we show that the fractional Fourier transform is nothing more than a variation of the standard Fourier transform and, as such, many of its properties, such as its inversion formula and sampling theorems, can be deduced from those of the Fourier transform by a simple change of variable.
179 citations
IBM1
TL;DR: A new approach to the computation of the discrete Fourier transform (DFT) with significantly reduced number of multiplication operations; it does not increase the number of addition operations in many cases.
Abstract: Recently, Dr. Shmuel Winograd discovered a new approach to the computation of the discrete Fourier transform (DFT). Relative to fast Fourier transform (FFT), the Winograd Fourier transform algorithm (WFTA) significantly reduces the number of multiplication operations; it does not increase the number of addition operations in many cases. This paper introduces the new algorithm and discusses the operations comparison problem. A guide for programming is included, as are some preliminary running times.
178 citations