Proceedings ArticleDOI
Fast interpolation of bandlimited functions
Samuel F. Potter,Nail A. Gumerov,Ramani Duraiswami +2 more
- pp 4516-4520
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TLDR
This work extends a recent method for computing a periodized fast multipole method with an adaptive algorithm that reduces the required number of multipole-to-local and local- to-local translations by an order of magnitude, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms.Abstract:
The nonuniform fast Fourier transform comprises a set of algorithms which approximately interpolate the usual discrete Fourier transform in the time and/or frequency domain. A nonuniform fast Fourier transform based on the fast multipole method was previously developed but passed over in favor of other approaches [1, 2]. This work extends a recent method for computing a periodized fast multipole method [3] with an adaptive algorithm that reduces the required number of multipole-to-local and local-to-local translations by an order of magnitude. This combination improves the speed and accuracy of the original algorithm, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms. Numerical experiments are carried out comparing our implementation with others, demonstrating its viability.read more
Citations
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Journal ArticleDOI
Efficient simulation of non-stationary non-homogeneous wind field: Fusion of multi-dimensional interpolation and NUFFT
TL;DR: In this paper , a multi-dimensional interpolation is used to decouple the evolutionary spectra accompanied by the application of non-uniform FFT (NUFFT) to expedite the simulation.
Journal ArticleDOI
Towards an Improvement of Fourier Transform
TL;DR: A new Fourier transform which is called Non Uniform Fourier Transform (NUFT), which takes into consideration the change of point index, and the experimental results prove the effectiveness of the proposed descriptor.
Book ChapterDOI
Sampling Theory in a Fourier Algebra Setting
TL;DR: The Fourier algebra has been studied in a variety of function spaces, including bandlimited and bandpass sampling as discussed by the authors, and it has been shown that approximate sampling has a place in Fourier algebras.
Proceedings ArticleDOI
A Fast Algorithm for SAR Imaging of Ground Moving Target Based on TRP-DPT and NUFFT
TL;DR: In this article , a fast algorithm for SAR imaging of ground moving target based on time-reversal process (TRP), discrete polynomial phase transform (DPT), and non-uniform Fourier transform (NUFFT) is proposed.
References
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Calculation of a constant Q spectral transform
TL;DR: In this article, a constant Q transform with a constant ratio of center frequency to resolution has been proposed to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components.