| The amount and shape of filter ringing is directly related to the filter frequency response and type of phase response. For example, for linear-phase filters, pre-ringing is equal to post-ringing, and they are completely determined by the filter frequency response. For minimum-phase filters, pre-ringing is minimal or absent, and post-ringing is maximal, and again they are completely determined by the frequency response (because phase response is also determined by the frequency response).
As a general rule, ringing occurs near discontinuities or bends in frequency response (and phase response). So, having smoother frequency response produces less ringing. Ringing should not be considered only as "undesirable artifact" of a filter, because it just reflects the desired frequency response. If the required frequency response is completely specified, there's no way to reduce the amount of ringing: you can only trade pre-ringing for post-ringing by choosing the type of filter phase response. |