Recursive digital filter synthesis in the time domain

The nonlinear minimization problem that results from recursive digital filter design with phase constraints is simplified somewhat by working in the time domain. This paper describes techniques that utilize the time samples of the desired response as target values for an iterative minimization. Initial values for the α and β (feedforward and feedback) coefficients can be obtained by one of several reliable methods and fed into iterative routines that lead to a locally optimal solution for the coefficients. The initial guess procedures, stemming from regressionlike equations, only require the solution of a set of linear equations. In addition, the iteration procedures described in this paper lead to recursive filter designs requiring little computer time. Examples are presented to illustrate a range of applications.