I believe magnitude (volume) and phase are sufficient to completely describe a discrete audio signal. If your filter can't change at least one of those, it can't actually change the signal at all.
If you mean "can you isolate the ringing of a linear-phase filter", then you can try applying the filter to an impulse (pick a sampling rate), then subtract the result from the impulse.
Gibbs looks like ringing, but is the proper result for limited bandwidth. In addition steep digital filters can ring if there is signal in the transition band between flat response and cutoff. Yes a square wave would cause actual ringing. If it had been thru an ADC the filtering would remove signals from the transition band. So the square wave would have Gibbs, but not frequencies to ring a digital filter.
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