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

Tim Ressel timr at circuitabbey.com
Wed May 17 02:48:22 CEST 2017

```That explains it. There was a girl in my high school trig class that
liked tight sweaters...

--tr

On 5/16/2017 9:13 AM, Donald Tillman wrote:
>> 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)
>
>     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
>
>
>
>
>
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--
--Tim Ressel
Circuit Abbey
timr at circuitabbey.com

```