simple way to add harmonics to a fundamental signal

[Martin Czech]

>> >What about LM1496-type ringmodulators, I've a neat schematic for a
> >dc-coupled ringmodulator at my website, two of these properly cascaded will
> >give you x^2 and x^3 at the simultaneously. 
> 
> I dont know enough trig for this..
> I know that putting the same sine wave into a multiplier gives a sine at twice
> the frequency, but what does one do for the 3f? anything simpler than just 
> multiply 2f and 3f and cancel out the f component?
> In the Burr Brown nonlinear handbook there are fairly exotic feedback loops with
> a multiplier in, to give things like trig approximations..
> 
(sin(x))**2=0.5*(1-cos(2x))
(sin(x))**3=0.25*(3*sin(x)-sin(3x))
(sin(x))**4=0.125*(cos(4x)-4*cos(2x)+3)

You see that you need some linear combination of sin(x)**n
in order to isolate , say a cos(nx).

This is what the Tchebycheff polynomes do.

m.c.