Recursive digital filter optimization based on simultaneous approximation in frequency and time domains

This work considers two appropriate optimization approaches for one-dimensional recursive digital filter design when the different requirements for magnitude, group delay and step responses are specified. The simultaneous approximation design in time and frequency domains is stated as a vector optimization problem. The objective functions are defined as a least square error between the approximated characteristic and a desired target function. The other approach used to solve the simultaneous approximation is the semi-infinite optimization problem, where the functional constraints are defined by group delay and step response.