simple way to add harmonics to a fundamental signal

[Martin Czech]

> > Nevertheless, it could be interesting to have such a polynome
> > approximation network driven with sine waves of varying amplitude,
> > ie. envelope or such.
> >
> > This would mean going from sine to some distorted product.
> >
> > And you have only "one knob" to turn: amplitude.
> 
> Ah! now I've lost track again. Could you expand a little on this last
> comment?
> 

Ok, we have a nonlinear network reproducing more or less some polynome function:

f(x)=a(n)*x**n+a(n-1)*x**(n-1)+a(n-2)*x**(n-2)+...+a(0)

where the a(n),a(n-1)...a(0) are real constant numbers, the coefficients,
a(0) often being 0 (dc offset).  If we choose the coefficents in the right
manner (Chebycheff) we get isolated harmonics out of the network if we
feed a sine wave in.

If we use other coefficients we get a harmonic wave with severall
harmonics.

Anyway, if the amplitude of our sine input changes, the harmonic content
of the output will change also.

Just think of f(x)=x**3 for example.  For very small input amplitudes
the output will look much like a sine wave, but for large signals it
surely won't.

This means we have a simple waveshaping synthesis with only one parameter:
input amplitude. This could be done via  potentiometer or a envelope etc. and vca.

Of course we could also change the coefficients, via potentiometer or vca.

Now, what about feeding some additional dc offset into the network?
This will change the part of the curve that is "used" by the sine.

What about using a couple of sine waves? 
This will give intermodulation (sum and difference frequencies).

What about using other wave forms as input (note: rectangular waves
will allways look rectangular, you can't really shape them).

What about using filters before or after the network?

What about including the network into a feedback path?


There are a lot of possibilities.

There are of course other waveshaping circuits, like PWM, multiple
comparators etc., but the polynomes have some softness, they don't sound
too sharp. It is a good question if approximations of polynomes are
able to keep this softness feature.


m.c.