Walsh function website update

[Neil Johnson]

Received: from [193.35.220.1] by esprit.camcon.co.uk with SMTP
  (IMA Internet Exchange 1.04b) id 5d80e901; Mon, 17 Aug 98 12:05:52 +0100
Received: from ganymede.co.uk by camcon.co.uk (SMI-8.6/SMI-SVR4)
	id MAA21602; Mon, 17 Aug 1998 12:06:49 +0100
From: jorgen.bergfors at idg.se
Received: by ganymede.co.uk (4.1/SMI-4.1)
	id AA07052; Mon, 17 Aug 98 12:06:44 BST
Received: from unknown(193.13.235.140) by ganymede.camcon.co.uk via smap (V1.3)
	id sma007046; Mon Aug 17 12:06:39 1998
Message-Id: <TFSKGVGE at idg.se>
Date: Mon, 17 Aug 1998 13:00:13 +0100
To: Neil.Johnson at camcon.co.uk, synth-diy at mailhost.bpa.nl
Subject: Re: Re[2]: Walsh function website update
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
X-Mailer: TFS Gateway /310000000/310100001/310100002/310260001/
-------------- next part --------------
     Jorgen,
     
     At a simple level, yes you can do it just with square waves.  However, 
     Walsh functions are much more powerful, in that you can, as for 
     Fourier functions, synthesize almost any waveform you care to create.  
     The square waves you mention, which can also be described as 
     Rademacher functions, form an incomplete set, limiting the number of 
     waveforms you can create.
     
     Its all in the maths really.
     
     And yes, the technology has been around for a long time!  The origin 
     of Walsh functions dates back to the late 1800's when engineers were 
     working out the best way to arrange telephone wires on telegraph 
     poles.  It was only until 1923 when Mr. Walsh documented them that 
     some mathematical description was available.
     
     Neil
     ----


______________________________ Reply Separator _________________________________
Subject: Re: Re[2]: Walsh function website update
Author:  jorgen.bergfors at idg.se at Internet-PO
Date:    17/08/98 13:00


Isn't this just adding square waves, like they used to do with electronic 
organs back in the 70s? Wersi did this, to get a sawtooth from a top octave and 
octave divider tone generator. 
I modified the Elektor electronic piano, which used square waves, by ORing with 
an octave higher. That created a 25% duty cycle pulse, which sounded better. I 
even ORed the higher octave vith a constant 1 or 0 so I could switch between 
the waveforms. This was around 1980.
     
/Jorgen