NFFT is a software library, written in C, for computing non-equispaced fast Fourier transforms and related variations. It implements the following transforms:
Non-equispaced fast Fourier transform (NFFT)
- forward transform (NFFT), i.e. frequency to time/space domain
- adjoint transform (adjoint NFFT), i.e. time/space to frequency domain
Generalisations
- to arbitrary nodes in time and frequency domain (NNFFT)
- to real-valued data, i.e. (co)sine transforms, (NFCT, NFST)
- to the sphere S^2 (NFSFT)
- to the rotation group (NFSOFT)
- to the hyperbolic cross (NSFFT)
Generalised inverse transformations based on iterative methods, e.g. CGNR/CGNE
Some examples for application of these transforms are provided:
Medical imaging
- magnetic resonance imaging (mri)
- computerised tomography (radon)
Summation schemes
- fast summation (fastsum)
- fast Gauss transform (FGT)
- singular kernels
- zonal kernels
polar FFT, discrete Radon transform, ridgelet transform
Detailed API documentation in HTML format can be found in
doc/html/index.html, if you are working from a release tarball.
When working from a source repository, the documentation can be
generated with Doxygen (which requires the doxygen-latex and perl packages):
make doc
The NFFT depends on the FFTW library, which is available for many Linux distros, Homebrew on macOS and MSYS2 on Windows. If you compile the FFTW yourself, it should be configured with the flag --enable-shared (and --enable-threads for the multi-threaded version). Building the NFFT requires make and a C compiler such as gcc.
When working from a source repository, you need to run libtoolize and autoreconf first. A bash script to do this is provided. This step requries the tools autoconf, automake and libtool.
./bootstrap.sh
The rest of the build process is standard.
./configure --enable-all --enable-openmp [add options as necessary, see below]
Alternatively, you might run the configure script for Matlab.
./configure --enable-all --enable-openmp --with-matlab=/path/to/matlab
Here are some useful optional flags for ./configure:
--enable-allspecifies that all modules should be compiled,--enable-openmpenables the multicore support and--enable-juliaspecifies that the julia interface will be compiled.--with-matlab=/path/to/matlabspecifies the path of a Matlab installation, and--with-octave=/path/to/octavedoes the same for GNU Octave.- For a list of all available options, run
./configure --help.
Build the software.
make
Optionally, unit tests may be run. Some of the unit tests require an installation of cunit.
make check
Optionally, install NFFT on your system.
make install
The current general paper, the one that we recommend if you wish to cite NFFT, is Keiner, J., Kunis, S., and Potts, D. ''Using NFFT 3 - a software library for various nonequispaced fast Fourier transforms'' ACM Trans. Math. Software 36, Article 19, 1-30, 2009. BibTeX entry:
@article{KeKuPo09,
author = {Jens Keiner and Stefan Kunis and Daniel Potts},
title = {Using {NFFT3} - a Software Library for Various Nonequispaced Fast {Fourier} Transforms},
journal = {{ACM} Trans. Math. Software},
year = {2009},
volume = {36},
pages = {Article 19, 1--30},
doi = {10.1145/1555386.1555388}}
Your comments are welcome! This is the third version of the library and may not be as robust or well documented as it should be. Please keep track of bugs or missing/confusing instructions and report them in our issue tracker or directly to Daniel Potts. The postal address is
Prof. Dr. Daniel Potts
TU Chemnitz, Fakultaet fuer Mathematik
Reichenhainer Str. 39
09107 Chemnitz
GERMANY
Alternatively, you might contact Stefan Kunis or Jens Keiner.
If you find NFFT useful, we would be delighted to hear about what application you are using NFFT for!
Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
This software was written by Jens Keiner, Stefan Kunis and Daniel Potts. It was developed at the Mathematical Institute, University of Luebeck, and at the Faculty of Mathematics, Chemnitz University of Technology.
NFFT3 is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. If not stated otherwise, this applies to all files contained in this package and its sub-directories.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
| File/Folder | Purpose |
|---|---|
| 3rdparty (dir) | Third-party source code |
| aclocal.m4 | Macros for configure script |
| applications (dir) | Application programs (see 4) above) |
| AUTHORS | Information about the authors of NFFT |
| bootstrap.sh | Bootstrap shell script that call Autoconf and friends |
| ChangeLog | A short version history |
| config (dir) | Used by configure script |
| configure | Configure script (created by calling ./bootstrap.sh) |
| configure.ac | Autoconf configure script template |
| CONVENTIONS | Internal coding conventions |
| COPYING | Information about redistributing NFFT |
| doc (dir) | User and developer documentation |
| examples (dir) | Simple examples for using NFFT routines |
| include (dir) | Header files |
| INSTALL | Installation instructions |
| julia (dir) | Julia interface for nfft |
| kernel (dir) | Source code for core library routines |
| Makefile.am | Automake Makefile template |
| Makefile.in | Makefile template generated from Makefile.am, processed by configure script |
| matlab (dir) | Matlab MEX interfaces for nfft, nfsft, nfsoft, nfft |
| NEWS | New and noteworthy |
| README | This file |
| README.md | This file |
| tests (dir) | CUnit tests |