[sdiy] Reverse Walsh?

[Ethan Duni]

At 12:03 PM 3/14/2002, you wrote:
>Is there something like FFT for Walsh that given an
>input curve, the ouput is a set of Walsh function
>coefficients?

-Yes! Its full name is the "Walsh-Hadamard Transform" or WHT for short. the
analysis equation for the WHT is (hopefully you can read my ascii-math
notation):

S[k] = (1/sqrt(N))*sum(s[n]*(-1)^b(k,n)), where the sum is over n from 0 to
N-1 and the results would be computed for coefficients k=0 through N-1. The
function b(k,n) controls the "sequency" of the basis function, and so its
value is the number of transitions basis vector k would have made at time n.
For more detailed info, look for books on transform coding. Also, the WHT
is, happily, a "fast" transform, like the FFT.

Ethan