[sdiy] XOR as 'digital' ring modulator

[Magnus Danielson]

On 11/09/2010 08:26 PM, Tom Wiltshire wrote:
> Hi again,
>
> Continuing the series of "things Tom doesn't understand that he'd like to get cleared up for once and for all", I've got another question.
>
> I've read in a couple of places (quoted below) that an XOR gate is not strictly equivalent to a ring modulator.
>
> Wikipedia says: "Though not equivalent to ring modulation, with square waves the resulting sound is quite similar." (Stinks of fudge to me!)
>
> Hal Chamberlin says (about the Rhodes Chroma): "The ring modulator is really just an exclusive-or digital gate (using CMOS logic that provides exact 5V amplitude outputs) and generates true ring modulation only when the input waveforms are square. Nevertheless, the audible effect of ring modulation is adequately produced even when the signals are nonsquare."
>
> The output from an XOR can be viewed like this:
>
> 	A	B	Q
> 	-1	-1	1
> 	-1	1	-1
> 	1	-1	-1
> 	1	1	1
>
> This looks to me like it's a perfect ring mod (multiplication function) as long as you stick to digital signals, square or otherwise. So XOR could multiply two PWM'd pulse trains no problem according to me, but not according to Chamberlin.
>
> So what am I missing?!

It sounds plain awful? :)

I agree, it's a 1 bit multiplication. Technically it would be XNOR but 
it is of little matter. But a ring-modulation has a "linear" response, 
so it would require more bits and the XOR doesn't match up.

For me the XOR "ring-mod" isn't the sound I usually want. It was a 
relief to finally get the pure ring-mod sound you get from a real ring 
mod and sine on one of the inputs.

Anyway, the XOR is not a ring-mod, but it is a 1 bit 4-quadrant 
multiplication... which for digital signals end up being the same.

Cheers,
Magnus