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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TL;DR: Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented andumerical results are given to confirm the efficiency.
Abstract: Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented. The computational procedure is based on approximation using a local Taylor series expansion and the fast Fourier transform (FFT). The forward transform for nonequispaced points is computed as the solution of a linear system involving the inverse Fourier transform. This latter system is solved using the iterative method GMRES with preconditioning. Numerical results are given to confirm the efficiency of the algorithms.
74 citations
03 Apr 1990
TL;DR: Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those forThe discrete Fourier transform (DFT) are developed and can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain.
Abstract: Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those for the discrete Fourier transform (DFT) are developed. The relations are valid if the filter frequency response is real and even. Two fairly simple relations are developed. The multiplication of the DCT of signal sequence and the DFT of filter sequence results in circular convolution of the folded signal sequence and the filter sequence. Thus, it can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain. >
73 citations
01 Jan 2001
TL;DR: The example of the musical score indicates that a reasonable and useful form of time-frequency analysis should still be possible and realizable.
Abstract: We have seen that ideal time-frequency analysis faces a fundamental obstacle in the form of the uncertainty principle. Nevertheless, the example of the musical score indicates that a reasonable and useful form of time-frequency analysis should still be possible and realizable.
73 citations
Book•
17 Jan 1989
TL;DR: In this article, the Fourier transfer FORTRAN subroutine is used to transfer a Fourier transform from a distribution to a discrete Fourier Transform (DFT) sample.
Abstract: Basic mathematical background integration theory distribution theory the Fourier series: the Fourier transform Fourier transform of a distribution the discrete Fourier transform sampling theory. Appendix: Fourier transfer FORTRAN subroutine.
73 citations
TL;DR: The architecture for a radix- R fast Fourier transform algorithm using a residue number system over Z[\omega] , where \omega is a primitive R th root of unity, is developed; and range and error estimates for this algorithm are derived.
Abstract: A new method is described for computing an N = R^{m} = 2^{\upsilon m} -point complex discrete Fourier transform that uses quantization within a dense ring of algebraic integers in conjunction with a residue number system over this ring The algebraic and analytic foundations for the technique are derived and discussed The architecture for a radix- R fast Fourier transform algorithm using a residue number system over Z[\omega] , where \omega is a primitive R th root of unity, is developed; and range and error estimates for this algorithm are derived
73 citations