Why do I see ringing in the output of a digital filter with a narrow transition band?
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.