Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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18 Jun 1996
TL;DR: It is found that for a certain dense set of fractional orders it is possible to define a discrete transformation and a fast algorithm is given, which has the same complexity as the FFT.
Abstract: Based on the fractional Fourier transformation of sampled periodic functions, the discrete form of the fractional Fourier transformation is obtained. It is found that for a certain dense set of fractional orders it is possible to define a discrete transformation. Also, for its efficient computation a fast algorithm, which has the same complexity as the FFT, is given.
28 citations
TL;DR: The aim of this paper is to show that the three widely and satisfactorily used techniques of Samulon, Nicolson, and Gans, which originate from apparently different ideas, are exactly the same.
Abstract: In 1965 Cooley and Tukey published an algorithm for rapid calculation of the discrete Fourier transform (DFT), a particularly convenient calculating technique, which can well be applied to impulse-like functions whose beginning and end lie at the same level. Independently, various propositions were made to overcome the truncation error which arises, if a step-like function, i.e. one whose end level differs from its starting level, is treated in the same way. It was argued that they behave differently under the influence of noise, band-limited violation, and other experimental inconveniences. The aim of this paper is to show that the three widely and satisfactorily used techniques of Samulon, Nicolson, and Gans, which originate from apparently different ideas, are exactly the same. An extended DFT and fast Fourier transform (FFT) formula is deduced which is adapted as well to impulse-like as to step-like functions.
28 citations
Posted Content•
TL;DR: In this paper, a different approach to the local Fourier transform is presented, which makes its properties almost tautological, and applies it to compute the local version of Katz's middle convolution.
Abstract: SBlock and HEsnault constructed the local Fourier transform for D-modules We present a different approach to the local Fourier transform, which makes its properties almost tautological We apply the local Fourier transform to compute the local version of Katz's middle convolution
28 citations
TL;DR: In this article, it was shown that a natural measure of spread for a periodic distribution follows simply upon regarding the distribution as a mass density on a ring, and that the centroid of this ring is expressed in terms of just a first moment, its distance from the geometric center gives a close analog of variance.
Abstract: A physicist’s intuition in Fourier theory is generally established from the parallels between Fourier series and transforms. Remarkably, one element of this theory that is especially significant in physics, namely the uncertainty principle, is never treated for Fourier series. We resolve this by first showing that a natural measure of spread for a periodic distribution follows simply upon regarding the distribution as a mass density on a ring. Even though the centroid of this ring is expressed in terms of just a first moment, its distance from the geometric center gives a close analog of variance. We then derive direct analogs of the uncertainty principle for both the Fourier series of a continuous periodic function as well as the fast Fourier transform of discrete data. The results have similar applications to those of the standard uncertainty principle.
28 citations
TL;DR: A new, fast and computationally efficient lateral subpixel shift registration algorithm is presented that reduces computation time and memory requirements without sacricing the accuracy associated with the usual FFT approach accuracy.
Abstract: A new, fast and computationally efficient lateral subpixel shift registration algorithm is presented. It is limited to register images that differ by small subpixel shifts otherwise its performance degrades. This algorithm significantly improves the performance of the single-step discrete Fourier transform approach proposed by Guizar-Sicairos and can be applied efficiently on large dimension images. It reduces the dimension of Fourier transform of the cross correlation matrix and reduces the discrete Fourier transform (DFT) matrix multiplications to speed up the registration process. Simulations show that our algorithm reduces computation time and memory requirements without sacricing the accuracy associated with the usual FFT approach accuracy.
28 citations