[sdiy] Reverse Walsh?

[Neil Johnson]

> Is there something like FFT for Walsh that given an input curve, the
> ouput is a set of Walsh function coefficients?

Yes, its called the Walsh Transform.  The reverse, used for synthesis (and
which has been recently discussed) is actaully the Inverse Walsh
Transform, much like the Inverse Fourier Transform.

The WT can be done with a delay line, some resistors and some op-amps
configured as difference amps.  This is ahow the WT was used in radar
systems -- a mercury delay line would shift the analogue data down the
line, with tap points going off to the op-amp matrix.  Needs quite a few
op-amps too.

There's some maths on my walsh page on my website (URL below).  Roughly,
each Walsh term is the sum of each tap multiplied by a Walsh function,
i.e. you add or subtract each sample to generate the Walsh coefficient.

Its a bit hairy, and a *lot* easier to do in a processor!

Hope this helps,
Neil

--
Neil Johnson :: Computer Laboratory :: University of Cambridge ::
http://www.njohnson.co.uk          http://www.cl.cam.ac.uk/~nej22
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