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: The purpose of this note is to show as clearly as possible the mathematical relationship between the two basic fast methods used for the calculation of discrete Fourier transforms and to generalize one of the methods a little further.
Abstract: The purpose of this note is to show as clearly as possible the mathematical relationship between the two basic fast methods used for the calculation of discrete Fourier transforms and to generalize one of the methods a little further. This method applies to all those linear transformations whose matrices are expressible as direct products.
137 citations
136 citations
TL;DR: This work improves well-known fast algorithms for the discrete spherical Fourier transform with a computational complexity of O(N2 log2 N), and presents, for the first time, a fast algorithm for scattered data on the sphere.
135 citations
TL;DR: This note makes a critical comparison of some matlab programs for the digital computation of the fractional Fourier transform that are freely available and describes the own implementation that lters the best out of the existing ones.
134 citations
TL;DR: In this article, a new procedure for calculating the complex, discrete Fourier transform of real-valued time series is presented for an example where the number of points in the series is an integral power of two.
Abstract: A new procedure is presented for calculating the complex, discrete Fourier transform of real-valued time series. This procedure is described for an example where the number of points in the series is an integral power of two. This algorithm preserves the order and symmetry of the Cooley-Tukey fast Fourier transform algorithm while effecting the two-to-one reduction in computation and storage which can be achieved when the series is real. Also discussed are hardware and software implementations of the algorithm which perform only (N/4) log2 (N/2) complex multiply and add operations, and which require only N real storage locations in analyzing each N-point record.
134 citations