NFFT – Nonequispaced FFT
NFFT is a software library, written in C, for computing non-equispaced fast
Fourier transforms and related variations. It implements the following
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
- 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:
- magnetic resonance imaging (mri)
- computerised tomography (radon)
- 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.
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
When working from a source repository, you need to run libtoolize and autoreconf first. A bash script to do this is provided.
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
--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 a path of Matlab, and
--with-octave=path/to/octavedoes the same for GNU Octave.
- For a list of all available options, run
Build the software.
Optionally, unit tests may be run.
Optionally, install NFFT on your system.
The most 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.
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 to
The postal address is
Prof. Dr. Daniel Potts TU Chemnitz, Fakultaet fuer Mathematik Reichenhainer Str. 39 09107 Chemnitz GERMANY
Alternatively, you might contact
If you find NFFT useful, we would be delighted to hear about what application
you are using NFFT for!
Legal Information & Credits
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
|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|
|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|
|tests (dir)||CUnit tests|