Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
On the numerical solution of the heat equation I: Fast solvers in free space
Journal of Computational Physics
A deterministic sub-linear time sparse fourier algorithm via non-adaptive compressed sensing methods
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast convolution with the free space Helmholtz Green's function
Journal of Computational Physics
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
Efficient thermal field computation in phase-field models
Journal of Computational Physics
Fast transform from an adaptive multi-wavelet representation to a partial Fourier representation
Journal of Computational Physics
The fractional Fourier transform and quadratic field magnetic resonance imaging
Computers & Mathematics with Applications
| Hi-index | 31.47 |
The nonequispaced or nonuniform fast Fourier transform (NUFFT) arises in a variety of application areas, including imaging processing and the numerical solution of partial differential equations. In its most general form, it takes as input an irregular sampling of a function and seeks to compute its Fourier transform at a nonuniform sampling of frequency locations. This is sometimes referred to as the NUFFT of type 3. Like the fast Fourier transform, the amount of work required is of the order O(NlogN), where N denotes the number of sampling points in both the physical and spectral domains. In this short note, we present the essential ideas underlying the algorithm in simple terms. We also illustrate its utility with application to problems in magnetic resonance imagin and heat flow.