Answer 2—The Gibbs phenomenon is strictly a function of the brick-wall, low-pass filter used to prevent aliasing within the system. It has nothing at all to do with either the sampling process or the quantization process.

It’s always taken for granted that the digital data represents samples of a properly band-limited analog signal. Even if you create an artificial digital signal such as (... +x, +x, +x, +x, –x, –x, –x, –x ...), the output contains such ringing because the DAC and its reconstruction filter produce the band-limited analog signal that could have produced the same set of samples. (In case you’re having trouble visualizing this, the samples occur at the exact instants that the ringing waveform crosses +x or –x.) The reconstruction filter is an important part of that process. To answer the final question, this is a good thing.

Contributor: David Tweed