[sdiy] Harmonic content of the "sigmoid" half-sine wave

[Aaron Lanterman]

On Jun 3, 2009, at 11:08 AM, Jerry Gray-Eskue wrote:

> It is also my understanding that if you mix 2 sine waves you get four
> frequencies out, the original frequencies, the sum of the  
> frequencies, and
> the difference of the frequencies. With each additional sine wave  
> added you
> get the same effect interacting with each of the other frequencies.

Careful here - there's two common uses of the term mixing. When people  
talk about building radios, "mixing" means multiplication. In audio  
circles, "mixing" means addition. (I got a lot of students annoyed at  
me one semester because I put an "audio mixer" on the final and a lot  
of the students thought it meant multiplication.)

The "mix 2 sine waves" you are referring to above is multiplication,  
not addition. If you mix two sine waves in terms of adding them, you  
just get two sine waves. :)

> So is the suggested fundamental not there, or is it created by the  
> total interaction of the original sine waves, their least common  
> fundamental frequency, ( even though not present in the generation  
> of the waveform ) and represented by the resulting wave form?

That can happen, but in the case of the particular "sigmoid" we were  
discussing the fundamentally really is there. The Fourier coefficient  
a_1 is nonzero.

- Aaron