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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the Fourier transform has been used for functional approximation and interpolation of stochastic processes, and it has proved of special use to statisticians concerned with stationary process data or concerned with the analysis of linear time-invariant systems.
Abstract: Publisher Summary The Fourier transform has proved of substantial use in most fields of science. It has proved of special use to statisticians concerned with stationary process data or concerned with the analysis of linear time-invariant systems. This chapter describes some of the uses and properties of Fourier transforms of stochastic processes. The Fourier transform turns up in the problems of functional approximation and interpolation. In seismic engineering, the Fourier transforms of observed strong motion records are taken as design inputs and corresponding responses of structures evaluated prior to construction. There are various classes of functions that may be viewed as subject to a harmonic analysis. Quite a different class of functions is provided by the realizations of stationary stochastic processes. Fourier transforms at distinct frequencies and based on nonintersecting data stretches may be approximated by independent normals. The variance of the approximating normal is proportional to the power spectrum of the series.
33 citations
TL;DR: In this paper, the fast Fourier transform algorithm was extended to the computation of Fourier transforms on compact Lie groups, and the basic technique uses factorization of group elements and Gel'fand-Tsetlin bases to simplify the computations.
Abstract: This article genralizes the fast Fourier transform algorithm to the computation of Fourier transforms on compact Lie groups. The basic technique uses factorization of group elements and Gel'fand-Tsetlin bases to simplify the computations, and may be extended to treat the computation of Fourier transforms of finitely supported distributions on the group. Similar transforms may be defined on homogeneous spaces; in that case we show how special function properties of spherical functions lead to more efficient algorithms. These results may all be viewed as generalizations of the fast Fourier transform algorithms on the circle, and of recent results about Fourier transforms on finite groups.
33 citations
22 Dec 1956
TL;DR: This note gives a method of proof of the sampling theorem, both for the case where the interval I is centered at the origin and where it is not, which is somewhat simpler than the previously given proofs, and at the same time is more rigorous, and yields several useful generalizations to functions of several variables and random functions.
Abstract: : The sampling theorem states essentially that if the frequency spectrum, or Fourier transform, g(w) of a time function f(t) vanishes for w outside some interval I , then f(t) is completely determined by its values at certain discrete sampling points, whose density is proportional to the length of the interval I . This note gives a method of proof of the sampling theorem, both for the case where the interval I is centered at the origin and where it is not, which is somewhat simpler than the previously given proofs, and at the same time is more rigorous, and yields several useful generalizations to functions of several variables and random functions.
33 citations
01 Jun 2014
TL;DR: In this paper, the discrete component of the nonlinear Fourier transform is studied and multi-eigen value signal sets are presented that achieve spectral efficiencies greater than 3 bits/s/Hz.
Abstract: Information transmission using only the discrete component of the nonlinear Fourier transform is studied and multi-eigenvalue signal sets are presented that achieve spectral efficiencies greater than 3 bits/s/Hz.
33 citations
TL;DR: In this article, it is shown that the maximum-likelihood estimation or robust estimation of the Fourier coefficients may be preferable to Fourier transformation if the noise contains outliers or is otherwise not normally distributed.
Abstract: It is shown that the maximum-likelihood estimation or robust estimation of the Fourier coefficients may be preferable to Fourier transformation if the noise contains outliers or is otherwise not normally distributed. The reason is that, in that case, these estimators produce Fourier coefficient estimates and, therefore, system parameter estimates having a smaller variance. >
33 citations