[sdiy] Ring Mod (was Re: Hadamard Transform Network)
Donald Tillman
don at till.com
Tue May 16 18:13:39 CEST 2017
> On May 16, 2017, at 8:40 AM, Tim Ressel <timr at circuitabbey.com> wrote:
>
> But you bring up an interesting point: 4QMs multiply, but they produce x+y, x-y tones. Anyone got the math on that?
High school trigonometry.
Trig identity:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Another trig identity, derivable from the first:
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
Add'm:
cos(a+b) + cos(a-b) = 2 cos(a)cos(b)
Your multiplication operation is on the right, your sum and difference tones are on the left.
-- Don
--
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com
More information about the Synth-diy
mailing list