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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
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Proceedings Article
01 Sep 2004
TL;DR: This paper analyzes a fast implementation of the Chirp transform, based on performing time-warping on the signal under analysis, combined with the Fast Fourier Transform.
Abstract: The Chirp transform is a powerful analysis tool for variable frequency signals such as speech. The computational load represents the main limitation of its original formulation, discouraging its use in real-time applications. This paper analyzes a fast implementation, based on performing time-warping on the signal under analysis, combined with the Fast Fourier Transform. The performance of the Fast Chirp transform depends on the one hand on the estimation of the time-warping operation based on the signal characteristics, and, on the other hand on the interpolation technique used for the warping. Observations from the analysis of speech signals support the method and the further lines.

18 citations

Patent
05 Nov 1998
TL;DR: In this paper, a pixel addressable spatial modulator is used to adjust the phase of the light of each pixel, which can be either a reflective or transmissive type device.
Abstract: A system that optically performs complex transforms, such as Fourier transforms. The system includes a pixel addressable spatial modulator that, in parallel, adjusts the phase of the light of each pixel. The modulator can be a reflective or transmissive type device. A transform lens, such as a Fourier lens, performs a two dimensional transform of the pixels outputs. This operation is repeated for the characteristic function (real and imaginary) of the function. The transformed outputs of the characteristic functions are sampled by a light detector and processed by a computer using simple fast operations, such as addition, into the final transform.

18 citations

Proceedings ArticleDOI
01 Mar 1984
TL;DR: The primary goals of these techniques are to eliminate unnecessary computations required when implementing a complex transform on a real-valued vector, to compute the transform in-place in the original length-N real vector, and to obtain the transform coefficients in-order.
Abstract: This paper presents two techniques for computing a discrete transform of a vector of real-valued data using the Prime Factor Algorithm (PFA) with high-speed convolution. These techniques are applied to the Discrete Fourier Transform (DFT) and the Discrete Hartley Transform (DHT). The primary goals of these techniques are to eliminate unnecessary computations required when implementing a complex transform on a real-valued vector, to compute the transform in-place in the original length-N real vector, and to obtain the transform coefficients in-order. The two algorithms described require modification of the Winograd short-length transform modules to accommodate a real input. One technique replaces the modules in the Burrus-Eschenbacher PFA program with the modified real-input modules and constructs the complete transform in a final step of additions and subtractions after modules for each factor have been executed. The other technique uses these real-input DFT modules for part of the computation associated with each factor and requires complex input DFT modules for another part of the computation. These algorithms require exactly one half of the number of multiplications and slightly less than one half of the number of additions required by a complex-input PFA.

18 citations

Journal ArticleDOI
TL;DR: In this paper, the power spectrum of a complex physiological system is estimated by smoothing the periodogram with the help of the fast Fourier transform algorithm, which can use either the whole record of the data or a number of disjoint records.
Abstract: . In this paper we consider techniques of spectral analysis for stationary point processes in order to study the behaviour of a complex physiological system. The estimates of the power spectrum are obtained by smoothing the periodogram which is computed very rapidly with the help of the fast Fourier transform algorithm. In the computation of the estimates we can use either the whole record of the data or a number of disjoint records.

18 citations

Proceedings ArticleDOI
01 Dec 2006
TL;DR: It is shown that Psi-densities can be determined using the efficient fast Fourier transform algorithm and their coefficients have an ordering with respect to the Hellinger metric and the multidimensional Bayesian estimator based on Fourier densities is derived in closed form.
Abstract: Efficiently implementing nonlinear Bayesian estimators is still an unsolved problem, especially for the multidimensional case. A trade-off between estimation quality and demand on computational resources has to be found. Using multidimensional Fourier series as representation for probability density functions, so called Fourier densities, is proposed. To ensure non-negativity, the approximation is performed indirectly via Psi-densities, of which the absolute square represent the Fourier density. It is shown that Psi-densities can be determined using the efficient fast Fourier transform algorithm and their coefficients have an ordering with respect to the Hellinger metric. Furthermore, the multidimensional Bayesian estimator based on Fourier densities is derived in closed form. That allows an efficient realization of the Bayesian estimator where the demands on computational resources are adjustable

18 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
20213
20201
20191
20189