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
15 Mar 1999
TL;DR: This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions and supports confidence that it will be accepted as the definitive definition of this transform.
Abstract: We propose and consolidate a definition of the discrete fractional Fourier transform which generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform (FRT) generalizes the continuous ordinary Fourier Transform. This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The fact that this definition satisfies all the desirable properties expected of the discrete FRT, supports our confidence that it will be accepted as the definitive definition of this transform.
210 citations
01 Jul 1966
TL;DR: The most common sampling errors are round-off of f(nT), truncation of the series generating f(t), aliasing of frequency components above half the sampling rate 1/T, jitter in the recording times nT, loss of a number of sampled values, and imperfect filtering in the recovery of f (t).
Abstract: A basic problem in signal theory is the reconstruction of a band-limited function f(t) from its sampled value f(nT). Because of a number of errors, the computed or physically realized signal is only approximately equal to f(t). The most common sampling errors are: round-off of f(nT), truncation of the series generating f(t), aliasing of frequency components above half the sampling rate 1/T, jitter in the recording times nT, loss of a number of sampled values, and imperfect filtering in the recovery of f(t). In the following we study the effect of these errors on the reconstructed signal and its Fourier transform.
207 citations
IBM1
TL;DR: In this article, the properties of the fast Fourier transform are related to commonly used integral transforms including the Fourier Transform and convolution integrals, and the relationship between the Fast Fourier Transformer and Fourier series is discussed.
Abstract: The fast Fourier transform is a computational procedure for calculating the finite Fourier transform of a time series. In this paper, the properties of the finite Fourier transform are related to commonly used integral transforms including the Fourier transform and convolution integrals. The relationship between the finite Fourier transform and Fourier series is also discussed.
206 citations
01 Oct 1973
TL;DR: The smoothed coherence transform is defined and examples of its uses and shortcomings are given and Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
Abstract: The smoothed coherence transform (SCOT) is defined and examples of its uses and shortcomings are given. Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
203 citations
TL;DR: The fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view and a course from the definition to the applications is provided, especially as a reference and an introduction for researchers and interested readers.
Abstract: The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
196 citations