[sdiy] Ring Mod (was Re: Hadamard Transform Network)

[Donald Tillman]

> 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