Method of synthesis of non-minimum-phase transfer functions for time-delay simulation

Abstract

The paper presents a new method for designing non-minimum phase rational approximants of the ideal delay function e−s suitable for the applications where the frequency spectrum of the input signal occupies large bandwidth. It is shown by theoretical considerations that for this purpose the most suitable type of delay characteristic is the one approximating to a constant delay over a frequency range extending from zero to a frequency ω < ωc and having a relatively large delay peak at the end of the passband (ωc). The amplitude of the initial transient ringing (precursor) and the overshoot in the transient response of the filter mainly depend on the value of the peak in the delay characteristic. The polynomials with two variable parameters that exhibit this type of delay response are then introduced and shown that the precursor and overshoot can be adjusted to any prescribed value by varying the free parameters. Extensive tables are presented enabling direct determination of the fourth-order transfer function with three right-half-plane zeros for almost any practical prescribed values of the precursor and overshoot. The method can be extended to higher-order networks and as an example a table containing data on the sixth-order functions with five right-half-plane zeros is also included. A comparison of the transient responses reveals that the technique proposed yields an improvement over all other methods so far described.