HAAR is a FORTRAN77 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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
HAAR is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
FFTPACK5.1, a FORTRAN77 library which implements the Fast Fourier Transform by Paul Swarztrauber and Dick Valent;
SFTPACK, a FORTRAN77 library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.
WALSH, a FORTRAN77 library which implements versions of the Walsh and Haar transforms.
WAVELET, a FORTRAN77 library which does some simple calculations with wavelet transforms;
You can go up one level to the FORTRAN77 source codes.