Faster 3D Walsh - Hadamard Transform (sequency, natural)

Implements a 3D Walsh Hadamard transform. This function is FAST!

Description

Copy&Paste from the file:
%WAT3D 3D Walsh or Hadamard Transform
% WAT3D(X, order) will transform the 3D matrix X to the Walsh or Hadmard
% domain depending on the parameter 'order'.
% If order == 'sequency' or 'walsh'
% The function will transform the matrix using the sequency ordered
% walsh functions.
% If order == 'hadamard' or 'natural'
% The function will transform the matrix using the natural ordered
% walsh functions. This is also known as the hadamard transform.
% TODO: order == 'dyadic' is not yet implemented.
% If no order is set the default 'sequency' is assumed.
%
% This function handles only the cases where N, N/12 or N/20
% is a power of 2 if order == 'natural' or 'hadamard'.
% If order == 'sequency' N must be strictly a power of 2.
    
% Reference:
% http://mathworld.wolfram.com/WalshFunction.html
% http://ieeexplore.ieee.org/iel5/12/35157/01674860.pdf
% http://dx.doi.org/ --> doi:10.1016/j.physletb.2003.10.071

This implementation is fast! I use it to call it many thousand times. It is way faster than the internal function (fwht).

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Faster 2D-Hadmard Tranform

• MATLAB release: MATLAB 7.7 (R2008b)