sftpack, a MATLAB code which carries out some "slow" Fourier transforms, that is, Fourier transforms without the techniques that allow for very fast computation.

The intention is to make the underlying calculation clear, and to provide a simple check and comparison of timing and usage for the fast calculations.

The fast Fourier transform is a highly efficient procedure. However, the coding of the algorithm, and the conventions for indexing, ordering, and normalization, can make it quite difficult to understand what is being done, or even to see how to use the software correctly. This means that a coding error or mistaken use can be undetected.


The computer code and data files described and made available on this web page are distributed under the MIT license


sftpack is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

c8lib, a MATLAB code which implements certain elementary functions for double precision complex variables;

cosine_transform, a MATLAB code which demonstrates some simple properties of the discrete cosine transform (dct).

fft_serial, a MATLAB code which demonstrates the computation of a fast fourier transform, and is intended as a starting point for implementing a parallel version.

haar, a MATLAB code which computes the haar transform of data.


sine_transform, a MATLAB code which demonstrates some simple properties of the discrete sine transform.

walsh, a MATLAB code which implements versions of the walsh and haar transforms.

wavelet, a MATLAB code which does some simple wavelet calculations;


  1. William Briggs, Van Emden Henson,
    The DFT: An Owner's Manual for the Discrete Fourier Transform,
    SIAM, 1995,
    ISBN13: 978-0-898713-42-8,
    LC: QA403.5.B75.
  2. Ralph Hartley,
    A More Symmetrical Fourier Analysis Applied to Transmission Problems,
    Proceedings of the Institute of Radio Engineers,
    Volume 30, 1942, pages 144-150.

Source Code:

Last revised on 12 March 2019.