Date:   1/29/2015 10:59:50 PM ( 9 y ago)
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URL:   https://www.curezone.org/forums/fm.asp?i=2233641

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>- do not cause "ringing at any and all frequencies."

Perhaps it should be looked at again.

>- You are confusing a periodic wave with an impulse, or infinite impulse in the FFT world.

No, that is entirely different. I am not speaking of Finite Impulse Response which is used in spectral analysis.

The tap of the leading edge can and does cause a slight ringing at any resonant frequency present but the frequencies that are not in synch with the harmonics quickly damp but the frequencies that are odd harmonics are reinforced.

Lab experiment:
If you drop a piano, every string will resonate for a short period of time due to the impact. The strings will still resonate for the short period of time even if the strings are out of tune. Also, even the wood pieces of the piano will each resonate although at greater dampening.

>- real world waveforms have lower amplitudes because the edges are not infinitely fast.

Yes, the limiting frequency range is directly related to the slew rate and there is a roll-off factor associated.

>- a triangle wave has no fast vertical edges, yet has same number of harmonics as a square-wave

Yes, but it can not cause non-harmonic resonating.

Tap any glass or metal pot with a knife and that object will ring for a short time.

>- Your view of how individual waves combine assumes that the rms values add linearly.

No such assumption. In fact if the square wave is a perfect 50 percent duty cycle, then all the sinusoidal wave forms of the odd harmonics will align in synchrony with the leading and trailing edges. Look at the illustrations in any mathematical book, electronics book, or physics book that discussed square waves.
 

Note that all of the sine waves cross the baseline at the same point that the square wave does, only at 50 percent duty cycle and only at 50 percent duty cycle is the resonance fully reinforced.

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