1D Walsh Transform

Function to generate a Walsh-Matrix one can use to do a 1D Walsh Transform

Description

This function generates a Walsh-Matrix which can be used to perform the 1D-Walsh transform on a vector:
Example:
>> walsh(4)*[1 2 3 4]'

The returned matrix is internally cached within the function (persistent) which implies that it is efficient to call the function in a loop as long as the arguments passed remain the same.

The transform is faster than other (loop-) implementations found here on the File Exchange since the loop induces a lot of overhead.

This file is actually just part of my 2D-Walsh-Transform file submission (ID 20312).

Type "help walsh" for help.

>> help walsh
 WALSH Hadamard matrix.
    WALSH(N) is a Walsh matrix of order N, that is,
    a matrix W with elements 1 or -1 such that W'*W = N*EYE(N).
    An N-by-N Walsh matrix with N > 2.
    This function handles only the cases where N is a power of 2.
    The function internally cashes the generated matrix so that
    it is efficient to call this function multiple times if the
    passed parameters remain the same among the calls.
 
    WALSH(N,CLASSNAME) produces a matrix of class CLASSNAME.
    CLASSNAME must be either 'single' or 'double' (the default).

Acknowledgements

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

• MATLAB release: MATLAB 7.6 (R2008a)

[lakshmi lakshmi]