Orpheus10, I don't think that a 'scope is the best way to investigate this.
I can clearly hear differences between waveforms that look identical on a scope, such as small differences in IM distortion. The resolution is simply not there. That may be because a scope's display is painted on a phosphor-coated screen, and it cannot react very fast. Only specialized phosphors are likely to react faster than 1KHz, much less 20 KHz. Knowing this, the scope's manufacturer is likely to have embedded averaging routines, so that one does not observe an event, but an average of events. Therefore, the question reduces to the temporal resolution of the instrument's display, as distinct from it's electronic frequency response to periodic waveforms repeated over thousands or millions of cycles. Alternately, specialized electronics "freezing" the action would work - but not a garden variety scope. Not being an expert, I may have got this part wrong - if so, please correct me.
I also note that consistency is a poor substitute for accuracy.
Second, digital representations of waveforms near the Nyquist criterion (half the sampling frequency) are aperiodic, except over several waves. To see this, consider a 20KHz sine wave being sampled at 44KHz. It is sampled, on average, at a rate of 44,000/20,000 = 2.2 times per wave. Since the wave evolves over a period of 2pi, the distance between two samples is 2pi/2.2 ~ 2.856. Without loss of generality, assume that the first sample is taken at point 0, the second at 2.856, the third at 5.712, etc. Then
Point Sin
0 0
2.8 .28
5.7 -.54
8.6 .76
11.4 -.99
14.3 .99
17.1 -.99
20 .91
22.8 -.76
25.7 .54
28.6 -.28
31.4 0
Which then repeats.
A linear interpolation of these points is the best a digital algorithm can do, unless it makes assumptions about the character and frequency of the waves. That linear interpolation results in asymmetrical triangular waveforms with peaks ranging from an absolute minimum of .28 to an absolute maximum of .99. The result is a waveform periodic over 5 of the original 20KHz waves, or 4KHz. Thus a 20KHz signal is rendered into a highly complex waveform which waxes and wanes over a 4KHz period. Furthermore, the waveform must be triangular and asymmetric, with attendant beats, unless heroic processing is invoked. And even if it is, that 20KHz tone must wax and wane over a 12dB range.
Clearly the effect worsens as one approaches the Nyquist frequency. The brick wall filters which prevent signals higher than Nyquist also impose their own distortions and phase shifts at lower frequencies, but that is another matter.
Finally, thank you Learsfool, for supporting my point about different types of distortion, especially those which have yet to be characterized. I think you may have said it better.
