Am 13.06.2018 um 15:01 schrieb Niels Dettenbach:

By theory, any square wave could be constructed by a infinite number of
(sinus) signals, while many of that images seems like produced from a finite
number of such "signal parts". this means - if i think correctly - a really
perfect square would have "infinite energy" required (pls correct me, if i'm
wrong here).

To get a good sqare, it is nearly impossible to get this by sinus overlay, since this does not converge well enough. You might get an impression here, where I show some additive synthesis:

But:

regarding the ear and hearing up to only 20kHz it is very well possible to synthesize a "sqare like" sound with only harmonics up to 20kHz. This works even better, since the filters in our system to not have to be neutral against the very high frequencies coming with a digital square wave.

so, what we hear when using real squares from a digital pin is mainly the summed up artifacts caused by the filters, the transmission and finally the loudspeakers.

What we also have to take into account when comparing waves:

Somtimes we can hear even ultrasonic waves, since they do have an impact on the membrane and littel bones in our ear. it is a kind of masking at high levels, so the sound impression is sightly different with / without utrasonic waves.

So in theory it should be right to generally provide frequencies of the real live up to 50kHz and above when replaying sound, but practically this required other hardware to do so.

I always recommend to limit the specttru down to 16-18kHz.

On the other hand: Feed hard squares into the filters might be used in sound synthesis for intended effects:

As you pointed out, more harmonics mean "more energy" and the non linearity and imperfectnes of all filters and systems will definitly cause impact on the final sound - also in der audible region.

J├╝rgen

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