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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.


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Journal ArticleDOI
TL;DR: The resulting adaptive STFT shares many desirable properties with the adaptive CKD, such as the ability to adapt to transient as well as long-term signal components, making it competitive in complexity with nonadaptive time-frequency algorithms.
Abstract: This article presents a method of adaptively adjusting the window length used in short-time Fourier analysis, related to our earlier work in which we developed a means of adaptively optimizing the performance of the cone kernel distribution (CKD). The optimal CKD cone length is, by definition, a measure of the interval over which the signal has constant or slowly changing frequency structure. The article shows that this length can also be used to compute a time-varying short-time Fourier transform (STFT). The resulting adaptive STFT shares many desirable properties with the adaptive CKD, such as the ability to adapt to transient as well as long-term signal components. The optimization requires O(N) operations per step, less than the fast Fourier transform (FFT) used in computing each time slice, making it competitive in complexity with nonadaptive time-frequency algorithms.

51 citations

Journal ArticleDOI
TL;DR: An algorithm is proposed to reconstruct two-dimensional wave-front from phase differences measured by lateral shearing interferometer based on double-grating that allows large shear amount and works fast based on fast Fourier transform.
Abstract: An algorithm is proposed to reconstruct two-dimensional wave-front from phase differences measured by lateral shearing interferometer. Two one-dimensional phase profiles of object wave-front are computed using Fourier transform from phase differences, and then the two-dimensional wave-front distribution is retrieved by use of least-square fitting. The algorithm allows large shear amount and works fast based on fast Fourier transform. Investigations into reconstruction accuracy and reliability are carried out by numerical experiments, in which effects of different shear amounts and noises on reconstruction accuracy are evaluated. Optical measurement is made in a lateral shearing interferometer based on double-grating.

51 citations

Journal ArticleDOI
TL;DR: An advanced Radon transform is developed using a multilayer fractional Fourier transform, a Cartesian-to-polar mapping, and 1-D inverse Fourier transforms, followed by peak detection in the sinogram.
Abstract: The Hough transform (HT) is a commonly used technique for the identification of straight lines in an image. The Hough transform can be equivalently computed using the Radon transform (RT), by performing line detection in the frequency domain through use of central-slice theorem. In this research, an advanced Radon transform is developed using a multilayer fractional Fourier transform, a Cartesian-to-polar mapping, and 1-D inverse Fourier transforms, followed by peak detection in the sinogram. The multilayer fractional Fourier transform achieves a more accurate sampling in the frequency domain, and requires no zero padding at the stage of Cartesian-to-polar coordinate mapping. Our experiments were conducted on mix-shape images, noisy images, mixed-thickness lines and a large data set consisting of 751 000 handwritten Chinese characters. The experimental results have shown that our proposed method outperforms all known representative line detection methods based on the standard Hough transform or the Fourier transform.

51 citations

Journal ArticleDOI
TL;DR: In this article, the authors study the impact of space variance on matched filtering and point out that space variance may be desirable under certain circumstances, and illustrate their theoretical conclusions by simulated experiments.

51 citations

Journal ArticleDOI
TL;DR: Alternative methods for the estimation of spectra are described and compared and general questions of statistical variability, the use of regression methods to smooth the periodogram, and use of time sectioning of the data to either smooth or to investigate non-stationarities in the data are discussed.

51 citations


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