# Minimal step response overshoot IIR notch filter design

Is there any IIR notch filter design algorithm, strategy or rule of thumb, that provides control for amount of overshoot/undershoot in step response of a filter?

• if the notch is 2nd-order, a biquad, i am sure that someone somewhere has worked out explicit closed-form expressions of the impulse response and the step response. from that you can derive overshoot. – robert bristow-johnson Sep 12 '17 at 19:00
• Here are some formulas for a biquad filter. I don't know of any design algorithm that imposes limits on overshoot/undershoot for the IIR case. You would need a non-linear optimization algorithm and you would have to deal with the problem of locally (but not globally) optimal solutions. – Matt L. Sep 12 '17 at 19:39
• wew! "$\sigma(n)$" for the Heaviside step function? that's a little unconventional, no? – robert bristow-johnson Sep 13 '17 at 5:58
• @robertbristow-johnson: Greek sigma for "S" for "step" ... variatio delectat. – Matt L. Sep 13 '17 at 6:20
• @MattL. Could you, please, provide a reference for the equation (1) from the answer (equation for a(n))? – Nikolai Popov Sep 13 '17 at 9:40