Closed form approach to minimax design of 1-dimensional recursive digital filters

Minimax design of 1-dimensional recursive digital filters is currently achieved by using iterative methods based on linear or nonlinear programming. These methods need extensive computation and their convergence cannot be always guaranteed. Based on the work of Antoniou on the design of elliptic 1-dimensional recursive digital filters, an approach is presented in the paper that provides the minimax design of 1-dimensional recursive digital filters satisfying prescribed specifications, in closed form. The amount of computation needed by the new approach is insignificant. The technique is applied to the design of a lowpass, a highpass, a bandpass and a bandstop filter.