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.
Papers published on a yearly basis
Papers
More filters
IBM1
TL;DR: Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
Abstract: A solution is given to the problem of deconvolving two time sequences using discrete Fourier transform (DFT) techniques when one of the sequences is of infinite duration. Both input- and impulse-response deconvolution problems are considered. Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
35 citations
TL;DR: Inverse Fourier transform has been used to derive the gradient-index profiles of inhomogeneous films having spectral requirements and results show a good agreement with the theory and evidences the reliability of the technology used to produce inhomogeneity media.
Abstract: Inverse Fourier transform has been used to derive the gradient-index profiles of inhomogeneous films having spectral requirements. Two examples are given, and the corresponding experimental designs are presented. Results show a good agreement with the theory and evidences the reliability of the technology used to produce inhomogeneous media.
35 citations
TL;DR: In this paper, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions, which are eigenfunctions of the continuous Fourier Transform and by performing a novel error-removal procedure.
Abstract: This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions, which are eigenfunctions of the continuous Fourier transform and by performing a novel error-removal procedure. Then, the result of the eigendecomposition of the DFT matrix is used to define a new DFRFT. Finally, several numerical examples are illustrated to demonstrate that the proposed DFRFT is a better approximation to the continuous fractional Fourier transform than the conventional defined DFRFT.
35 citations
TL;DR: It is shown that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT.
35 citations
TL;DR: By examining the various forms in which the Gabor equations can be expressed, it is discovered how the input, window, biorthogonal function, Gabor coefficients and Zak transforms map under periodization and sampling.
35 citations