Why do I see ringing in the output of a digital filter with a narrow transition band? I am doing some 'extreme' eq for spectral mangling type effects with audio. Im using brick wall filters, and very narrow band pass and reject filters (vst plugins), and I'd like to know if there's anything I can do about the pre/post 'ring' with the linear phase /minimal phase filters Im using.  Unfortunately I must use steep eq slopes . Im prepared to use minimum phase as it avoids pre-ring.

Specifically, Im wondering:


What exactly causes the oscilliations in the impulse response just after the input, in a a minimum phase filter?
Are these osccilations what causes the audible pre and post 'ringing' sound which is added to the passband with with steep slope filtering?
Are the oscilliations, and thus the ringing frequency always the same frequency, or does the ringing frequency depend in some way on the input signal?


Thanks very much for your expertise. I look forward to any responses.
Dale.
Your observations are an example of the Gibbs phenomenon. When you apply a filter with a very sharp transition band, you will observe oscillations in the filter output (or "ringing") near any sharp transitions in the input signal (e.g. boundaries of pulsed waveforms). The apparent "frequency" of the oscillations is dependent upon the bandwidth of the filter; as you increase the filter's cutoff frequency, the oscillations will become more localized in time (i.e. "higher in frequency"), but the peak overshoot does not change. The Wikipedia article linked above has a good explanation halfway through or so.