From: Chris Muir < cbm@... >
Subject: Re: 1 hard science question
Date: Thu, 3 Jul 2008 14:40:12 -0700
Message-ID: < AD7B588A-D181-4E0B-9557-3C1ADAA7CBAF@... >

>
> On Jul 2, 2008, at 9:20 AM, Monroe Eskew wrote:
>
> > Perhaps a sine wave can be expressed as an infinite series of square
> > waves.
>
> Aren't Walsh transforms squarewave-based

They are. Sine generation is possible but not *THAT* neat really.

Google the web for Walsh functions and sine and you should find several
relevant pages. Wikipedia should help you on the way as usual.

In short will all waveforms exist in sine and cosine form, i.e. 0 and 90
degrees. The simple 4 sample case is illustrative. These are the 4 base
vectors (the third line can be inversed, don't recall from the top of my head,
but literature will correct that mistake):

+1 +1 +1 +1
+1 +1 -1 -1
-1 +1 +1 -1
+1 -1 +1 -1

Looks simple and powerfull. Ah well. :)

Cheers,
Magnus