sqr

[Martin Czech]

> Here's one for the maths people:
> A ring modulator (multiplier chip) with identical sine waves at
> the 2 inputs produces a sine wave at double the frequency.
yes:

O=sin(a)*sin(b)=0.5*cos(a+b)+0.5*cos(a-b).
if a=b => O=1+0.5(cos(2a))

right, double Frequency.
> Now I assume it is possible to put a squarer (ie multiplier with tied
> inputs) in a feedback loop to give a square rooter... but what would the
> output look like? A sine wave at half the frequency? And what happens
> with a less simple input, eg a signal consisting of two sine waves at
> different frequencies?

Ok, lets suppose we have a square router.
O=sqr(sin(a)).
Now , first of all, we want to have real output, not complex.
So what are we going to do with the negative halve-wave of the sin?
And the positive halv-wave will be distorted.
I don't believe there is a theorem like above for muliplication or squaring,
i.e. we can only find a numeric solution. However, you'll end up with
a harmonic wave, lots of partials and never with half frequency or
something like that.

m.c.