Answer 7
The actual sampled data, represented by the square dots in the diagram, contains equal levels of F_signal (the sine wave) and F_sample-F_signal (one of the aliases of the sine wave). Any reconstruction filter is going to have difficulty passing the one and eliminating the other, so you inevitably get some of the alias signal, which, when added to the desired signal, produces the "modulation" you see.

In the case of a software display of a waveform on a computer screen (e.g., such as you might see in CoolEdit), they're probably using an FIR low-pass filter (sinx/x coefficients) windowed to some finite length. A shorter window gives faster drawing times, so they're making a trade-off between visual fidelity and interactive performance. The windowing makes the filter somewhat less than brick wall, so you get the leakage of the alias and modulation.

In the case of a real audio D/A converter, even with oversampling, you can't get perfect stopband attenuation (and you must always do at least some of the filtering in the analog domain). So, once again, you see the leakage and modulation.

In this example:

F_signal = 0.9×F_Nyquist

so,

F_alias = 1.1×F_Nyquist

To eliminate the visible artifacts, the reconstruction filter would need to have a slope of about 60dB over this frequency span, or about 200 dB/octave.

Contributor: Dave Tweed

Published February 2003