HAAR, a C++ 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 FORTRAN90 version and a MATLAB version and a Python version.
SFTPACK, a C++ library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.
SINE_TRANSFORM, a C++ library which demonstrates some simple properties of the discrete sine transform.
WALSH, a C++ library which implements versions of the Walsh and Haar transforms.