[sdiy] Taylor series and sums and difference tones

[Aaron Lanterman]

On Jun 4, 2009, at 3:31 PM, Ingo Debus wrote:

> I think this boils down to the question: are the systems involved  
> linear or not? If they are, then adding two sine waves gets you just  
> the sum of two sine waves. If the sum is sent through something  
> which is nonlinear, then components of other frequencies emerge.
> It doesn't matter if the system is mechanical or electronic. It only  
> matters if it's linear or not.

Excellent!!!

For nonlinear systems, you can think of expanding the nonlinearity in  
terms of a Taylor series, with constant, linear, squared, cubic,  
quartic, etc. terms.

If you think of putting a sum of two sinusoids into the nonlinearity,  
the squared term in the taylor series will give you these sum and  
difference tones.

But you'll also get all sorts of junk from the other terms.

- Aaron