Orthogonal Functions and Transforms
?n is generated by compression of ?[n/2] into its first half and ? ?[n/2] into its second half, and is even/odd as n.
To generate discrete Walsh functions, the number of samples (equispaced) should be 2n to satisfy the above requirement.
Walsh functions are ordered by the number of zero-crossings in the interval (0,1), called sequency.
If the Walsh functions with the number of zero-crossings ? (2n - 1) are sampled with N = 2n uniformly-spaced points, we get a square matrix representation, which is orthogonal with rows ordered with increasing number of zero-crossings.