HAAR
The Haar Transform

HAAR is a Python 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.

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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

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

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

Reference:

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

Source Code:

haar.py, the source code.
haar.sh runs all the tests.
haar.txt, the output file.

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