Fast Fourier Transforms for Nonequispaced Data: A Tutorial

By Daniel Potts, Gabriele Steidl, Manfred Tasche. 2001

351 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b8286cfb324be2162258decff7791d375b33d9bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Stochastic gravitational wave background from smoothed cosmic string loops (2017, methodology): “We use the method of Potts, Steidl, and Tasche [51].”
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms (2009, methodology): “This transform is known as fast Fourier transform for nonequispaced data in space and frequency domain (NNFFT) [Dutt and Rokhlin 1993; Elbel and Steidl 1998; Potts et al. 2001]”
Fast Fourier Transform (2011, methodology): “In a similar way as for the NFFT [111] we can develop fast algorithms for the computation of”
Robust numerical methods for contingent claims under jump diffusion processes (2005, background): “given unequally spaced data, determine the Fourier coefficients), as well as the forward FFT problem (given the Fourier coefficients, determine the inverse transform values on an unequally spaced grid) (see, for example Ware, 1998; Duijndam and Schonewille, 1999; Potts et al., 2001).”
A fast algorithm for nonequispaced Fourier transforms on the rotation group (2009, methodology): “In the following sections we will describe how to split up the NDSOFT (3.5) such that we can use the NFFT [14, 23] on one hand and a fast polynomial transform [7, 21] on the other hand for its evaluation.”
Compressive Sensing with structured random matrices (2012, neutral): “7) has a fast (approximate) matrix multiplication algorithm, called the non-equispaced fast Fourier transform (NFFT) [46, 101].”
Nonuniform fast Fourier transforms using min-max interpolation (2003, background): “Nevertheless, there may be other applications where “Problem 1” is the natural formulation, and for these problems, we recommend the general guidelines provided in reviews like [41].”
Numerical solution of two asset jump diffusion models for option valuation (2008, methodology): “There are several algorithms which can be used to determine the FFT of input data on unequally spaced grids [50, 17, 45].”
Accelerating the Nonuniform Fast Fourier Transform (2004, background): “This is of particular value in two- and threedimensional settings, saving either 10dN in storage in d dimensions or a factor of about 5–10 in CPU time (independent of dimension).”
Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach (2010, background): “D nonequispaced fast Fourier transform (NFFT - Potts et al., 2001; Kunis, 2006) along the spatial axis, Nx, and form a new operator B def = (Nx ⊗ Ft)T (3) that links curvelet coefficients to nonequispaced traces (Figure 3).”