WALSH
Walsh and Haar Transforms

WALSH is a MATLAB library which implements versions of the Walsh and Haar transforms.

Note that the programs, as printed in the reference, had a few typographical errors. Several programs, in particular FHT and FRT, could not be made to perform as described in the text, and hence have been omitted.

Licensing:

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

Languages:

WALSH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

HAAR, a MATLAB library which computes the Haar transform of data.

SFTPACK, a MATLAB library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

SINE_TRANSFORM, a MATLAB library which demonstrates some simple properties of the discrete sine transform.

WAVELET, a MATLAB library which does some simple wavelet calculations;

Reference:

1. Ken Beauchamp,
   Walsh functions and their applications,
   Academic Press, 1975,
   ISBN: 0-12-084050-2,
   LC: QA404.5.B33.

Source Code:

• ffwt.m performs an in-place fast Walsh transform.
• fwt.m performs a fast Walsh transform.
• haar.m performs a Haar transform.
• haarin.m inverts a Haar transform.
• hnorm.m computes the normalization factors for a forward or inverse Haar transform.
• i4_log_2.m returns the integer part of the logarithm base 2 of an I4.
• i4_modp.m returns the nonnegative remainder of integer division.
• i4_wrap.m forces an I4 to lie between given limits by wrapping.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• timestamp.m prints out the current YMDHMS date as a timestamp.
• walsh.m performs a fast Walsh transform.

Examples and Tests:

• walsh_test.m, a sample calling program.
• walsh_test_output.txt, the output file.
• walsh_test01.m, tests FWT.
• walsh_test02.m, tests WALSH.
• walsh_test03.m, tests HAAR, HAARIN and HNORM.
• walsh_test04.m, tests FFWT.

You can go up one level to the MATLAB source codes.