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

[Tom Wiltshire]

On 3 Jun 2009, at 17:36, Aaron Lanterman wrote:
>
>> 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 is dead right about the Sigmoid, but I think Jerry was talking  
about my  'pulse' examples. Sorry, I was sidetracking this  
conversation there...

I've made the following sigmoid:

http://www.electricdruid.com/Sigmoid.png

This was done by creating a standard ramp wave with 64 harmonics  
(where each harmonics amplitude is 1/h) and then boosting the level  
of the fundamental to 1.6 rather than 1. This can alternatvely be  
seen as scaling the other harmonics down a little bit. Either way,  
the sigmoid is a ramp with the harmonics backed off a little bit.

Regards,
Tom