I am looking for a C++ library for Discrete Wavelet Transform (DWT) which can also return the NxN DWT matrix of the transform. There was a similar question opened here
Looking for a good C/C++ wavelet library for signal processing
but I am looking for something more specific as you can see.
It would be more helpful if the library is under some non-GNU license that lets me use it in proprietary software (LGPL, MPL, BSD etc.)
Thanks in advance
The reason why this matrix is never computed is that it is very inefficient to compute the DWT using it. The FWT approach is much faster.
For a signal of length 16 and a 3-level haar transform, I found that this matrix in matlab
>> h=[1 1];
>> g=[1 -1];
>> m1=[[ones(1,8) zeros(1,8); ...
zeros(1,8) ones(1,8); ...
1 1 1 1 -1 -1 -1 -1 zeros(1,8); ...
zeros(1,8) 1 1 1 1 -1 -1 -1 -1]/sqrt(8); ...
[1 1 -1 -1 zeros(1,12); ...
zeros(1,4) 1 1 -1 -1 zeros(1,8); ...
zeros(1,8) 1 1 -1 -1 zeros(1,4); ...
zeros(1,12) 1 1 -1 -1]/sqrt(4); ...
[g zeros(1,14); ...
zeros(1,2) g zeros(1,12); ...
zeros(1,4) g zeros(1,10); ...
zeros(1,6) g zeros(1,8); ...
zeros(1,8) g zeros(1,6); ...
zeros(1,10) g zeros(1,4); ...
zeros(1,12) g zeros(1,2); ...
zeros(1,14) g]/sqrt(2)]
m1 =
A A A A A A A A 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 A A A A A A A A
A A A A -A -A -A -A 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 A A A A -A -A -A -A
B B -B -B 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 B B -B -B 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 B B -B -B 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 B B -B -B
C -C 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 C -C 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 C -C 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 C -C 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 C -C 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 C -C 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 C -C 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 C -C
where A=1/sqrt(8), B=1/sqrt(4) and C=1/sqrt(2).
corresponds to the FWT. That shows you how you build your matrix from the filters. You start with the bottom half of the matrix --a matrix of zeroes, putting filter g 2 steps further every row. then make the filter twice as wide and repeat, only now shift 4 steps at a time. repeat this until you are at the highest level of decomposition, the finally put the approximation filter in at the same width (here, 8).
just as a check
>> signal=1:16; % ramp
>> [h g]=daubcqf(2); % Haar coefficients from the Rice wavelet toolbox
>> fwt(h,signal,3) % fwt code by Jeffrey Kantor
>> m1*signal' % should produce the same vector
Hope that helps you writing it in C++. It is not difficult (a bit of bookkeeping) but as said, noone uses it because efficient algorithms do not need it.
