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: The result is able to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform.
Abstract: In [2] we have considered a class of integral transforms which generalizs the classical Fourier tranform. We are able now to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform. Furthermore, when our result is considered in connnection with the particular kernel associated with th Fourier transform, the fast Fourier transform algorithm can be used in order to approximate the Hermite-Fourier coefficients of a class of functions *
21 citations
TL;DR: A new fast Fouriertransform is proposed to recover a real non-negative signal xR+N from its discrete Fourier transform x=FNxCN if the signal x appears to have a short support, i.e., vanishes outside a support interval of length m.
21 citations
Patent•
30 Sep 1993TL;DR: In this paper, a signal detection system divides a data sampling run into blocks and perms a fast Fourier transform on each block, sorting results by frequency, and combines the results of results of the transform corresponding to each frequency to derive a test statistic which is unbiased by Gaussian noise.
Abstract: A signal detection system divides a data sampling run into blocks and perms a fast Fourier transform on each block, sorting results by frequency. Combinations of results of the fast Fourier transform corresponding to each frequency are processed to derive a test statistic which is unbiased by Gaussian noise while including such combinations of results of the fast Fourier transform which would be redundant over other combinations. Information concerning the frequency behavior of the signal derived in the course of detection, is accomplished with increased sensitivity.
21 citations
TL;DR: The effect of the fractional Fourier transform on homogeneous functions is discussed in this paper, where an application is made to the Mandelbrot-Weierstrass cosine fractal.
Abstract: The effect of the fractional Fourier transform on homogeneous functions is discussed. The fractional Fourier transform is used for the determination of the main parameters of fractals. An application is made to the Mandelbrot–Weierstrass cosine fractal. The results are applied to describe the propagation of a fractal field through quadratic refractive-index media and to determine its fractal dimension.
21 citations
TL;DR: This work combines two concepts: the joint transform correlator and the fractional Fourier transform and it is shown that this combination is almost as convenient experimentally as the classical joint Transform correlator.
Abstract: We combine two concepts: the joint transform correlator and the fractional Fourier transform. This combination is almost as convenient experimentally as the classical joint transform correlator. As a processor it is as versatile as the standard fractional Fourier correlator.
21 citations