haar, a C++ code 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 MIT 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++ code which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.
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WALSH, a C++ code which implements versions of the Walsh and Haar transforms.