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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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Journal ArticleDOI
TL;DR: In this article, the interpolated discrete Fourier transform (IpDFT) with maximum sidelobe decay windows is investigated for machinery fault feature identification, which combines the idea of local frequency band zooming-in with the IpDFTs and demonstrates high accuracy and frequency resolution in signal parameter estimation when different characteristic frequencies are very close.
Abstract: Complex systems can significantly benefit from condition monitoring and diagnosis to optimize operational availability and safety. However, for most complex systems, multi-fault diagnosis is a challenging issue, as fault-related components are often too close in the frequency domain to be easily identified. In this paper, the interpolated discrete Fourier transform (IpDFT) with maximum sidelobe decay windows is investigated for machinery fault feature identification. A novel identification method called the zoom IpDFT is proposed, which combines the idea of local frequency band zooming-in with the IpDFT and demonstrates high accuracy and frequency resolution in signal parameter estimation when different characteristic frequencies are very close. Simulation and a case study on rolling element bearing vibration data indicate that the proposed zoom IpDFT based on multiple modulations has better capability to identify characteristic components than do traditional methods, including fast Fourier transform (FFT) and zoom FFT.

35 citations

Patent
14 Nov 1991
TL;DR: In this article, a signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signals.
Abstract: A signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signal. The signal processing apparatus and method utilize a process in which a data set of samples is used to iteratively compute a set of frequency samples, wherein each computational iteration utilizes error information which is calculated between the initial data and data synthesized using the AFT. The iterative computations converge and provide AFT values at the Farey-fraction arguments which are consistent with values given by a zero-padded Discrete Fourier Transform (DFT), thus obtaining dense frequency domain samples without interpolation or zero-padding.

35 citations

Journal ArticleDOI
TL;DR: In this article, the Fourier series boundary element method (FBEM) is used to calculate the integrals over the angle of revolution (AoR) of each Fourier term.
Abstract: Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general.

35 citations

Journal ArticleDOI
TL;DR: A two-dimensional Fast Fourier Transform program written in C language was developed for the personal computer with the specific purpose of extracting periodicities from digital elevation model (DEM) data and provides insight to the nature and complexity of the terrain.

35 citations

Journal ArticleDOI
TL;DR: New algorithms for DFT(p; k), the discrete Fourier transform on a k-dimensional data set with p points along each array, where p is a prime are exhibited.
Abstract: We exhibit new algorithms for DFT(p; k), the discrete Fourier transform on a k-dimensional data set with p points along each array, where p is a prime. At a cost of additions only, these algorithms compute DFT(p; k) with (pk- 1)/(p - 1) distinct DFT(p; 1) computations.

34 citations


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