Does this suggest that electronic circuits naturally produce harmonics to the input frequency? That electrons themselves break up into lower order components?
Does the sin-cubed (and cos-cubed) function identity:
https://calculus.subwiki.org/wiki/Sine-cubed_function
suggest that spatially transmitted frequencies ought to be detected by some sort of Composite (or Complementary)-Fourier Transform, where instead of detecting 1 frequency transmitted at a time for a set binary signal, that we can actually take out known pieces of noise, these natural harmonics, and they would be improving to the signal-to-noise ratio?
Dear Aden
Here is my understanding
Harmonics are not created by inductance or capacitance. A combination of capacitance and inductance is just a filter which let pass certain frequencies and stop others. When capacitance and inductance are in series or in parallel the filter will let pass at a frequency called resonance which happen when XL=XC.
Harmonics are created by switching devices.
So if your circuit includes a junction with a voltage potential (ie a diode) then a periodic change in polarity will create harmonics which will in turn be conducted, stopped or amplified.
Emmanuel Orban de Xivry , yes, but if sin^3(x) = (3sin(x) - sin(3x))/4
Then 9sin(x) + 9 sin(9x) = 12 sin^3(x) - 4 sin^3(3x) -6 sin (3x)
So a 3 dimensional spherical wave needs a difference of three times the frequency and a third of the amplitude.
With nine times the frequency you can have a difference between two spherical waves of a third the amplitude and the frequency with a difference of a single dimensional wave at half the amplitude and a third of the frequency.
The shapes and the components go together, all you need are thirds of frequencies.
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