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The example is not recursive...

207.207.243.246

It is interative, but the reason I stopped at 1000 aliases is that at that point, the energy in an alias is very small, each alais (due to the step-function nature of the DAC output) is smaller and smaller...

There reason I didn't plot the last alias is that it's so small you can't see it on the scale of +-1.

When I say a sinewave must be of infinite length to have ONLY frequency content at the frequency of the sinewave, that's a simple, outright statement.

The problem with your example of a damped sine wave is that it has out-of-band content, i.e. content ABOVE the Nyquist limit, at least for most examples. (It would be possible to construct one that did not encroach, to a given error level, the area above 20khz, and that example would in fact work fine. Demonstrating it would be tougher, because one oculd not merely plot sine waves as aliases, but whole spectra as aliases (yes, they could be turned into a time waveform), and the nature of the signal wouldn't be nearly as obvious.

So, the last octave is FINE. That's what the example shows. It shows that any in-band signal is FINE. Period. (of course given competant filter design, which may not be an entirely safe assumption ;_(




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