HAAR
The Haar Transform

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

In the simplest case, one is given a vector X whose length N is a power of 2. We now consider consecutive pairs of entries of X, and for I from 0 to (N/2)-1 we define:

        S[I] = ( X[2*I] + X[2*I+1] ) / sqrt ( 2 )
        D[I] = ( X[2*I] - X[2*I+1] ) / sqrt ( 2 )

We now replace X by the vector S concatenated with D. Assuming that (N/2) is greater than 1, we repeat the operation on the (N/2) entries of S, and so on, until we have reached a stage where our resultant S and D each contain one entry.

For data in the form of a 2D array, the transform is applied to the columns and then the rows.

Licensing:

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

Languages:

HAAR 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:

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.

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

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

Reference:

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

Source Code:

haar_1d.m, computes the Haar transform of a vector.
haar_1d_inverse.m, inverts the Haar transform of a vector.
haar_2d.m, computes the Haar transform of a 2D array.
haar_2d_inverse.m, inverts the Haar transform of a 2D array.
r8mat_print.m, prints an R8MAT, with an optional title;
r8mat_print_some.m, prints some of an R8MAT;
r8mat_uniform_01.m, returns a unit pseudorandom R8MAT;
r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

haar_test.m, calls all the tests;
haar_test_output.txt, the output file.
haar_test01.m, tests HAAR_1D and HAAR_1D_INVERSE;
haar_test02.m, tests HAAR_2D and HAAR_2D_INVERSE;

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

Last modified on 15 March 2011.