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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12 May 1996
TL;DR: In this article, a new version of discrete fractional Fourier transform (DFRFT) was proposed, which provides similar transforms as those of continuous FRFT and also holds the rotation properties.
Abstract: The continuous fractional Fourier transform (FRFT) represents a rotation of signal in time-frequency plane, and it has become an important tool for signal analysis. A discrete version of fractional Fourier transform has been developed but its results do not match those of continuous case. In this paper, we propose a new version of discrete fractional Fourier transform (DFRFT). This new DFRFT will provide similar transforms as those of continuous fractional Fourier transform and also hold the rotation properties.
49 citations
49 citations
TL;DR: It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complexorder regime and the beam width of a Gaussian beam subjected to the complex- order Fouriertransform is obtained analytically with the ABCD matrix approach.
Abstract: It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complexorder regime. A complex-order Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while the optical implementation of fractional-order Fourier transform involves gradient-index media or spherical lenses, the optical interpretation of complex-order Fourier transform is practically based on the convolution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained analytically with the ABCD matrix approach.
49 citations
01 Jan 2000
TL;DR: A formula for computing the cross-cor correlation of a pair of images (and hence the auto-correlation of a single image) is presented, based on a previously published hypercomplex Fourier transform.
Abstract: The auto-correlation and cross-correlation function have been generalized to color images, but only by explicit evaluation of a double summation over the whole image for each pixel of the correlation result. Practical use of any correlation method on images of reasonable spatial resolution requires realization using a Fourier transform. A formula for computing the cross-correlation of a pair of images (and hence the auto-correlation of a single image) is presented, based on a previously published hypercomplex Fourier transform.
49 citations
TL;DR: An all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector based on a statistic, commonly called the F-statistic, derived from the maximum-likelihood principle is presented.
Abstract: We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector Our search is based on a statistic, commonly called the F-statistic, derived from the maximum-likelihood principle in Paper I of this series We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the F-statistic We present several algorithms to calculate efficiently this statistic In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform in calculation of the F-statistic We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies We present interpolation methods that approximately convert the two integrals in the F-statistic into Fourier transforms so that the fast Fourier transform algorithm can be applied in their evaluation We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes
49 citations