GENERATION OF DISCRETE AND CONTINUOUS-TIME TRANSFER-FUNCTION COEFFICIENTS

Given a continuous time transfer function g(s), this paper provides cl osed-form solutions for the coefficients of discrete time transfer fun ctions g(z). Similar solutions are also provided for g(s), given g(z). Three integration methods are used for each direction (termed forward and inverse, respectively) of transformation: (a) the 'forward rectan gular rule'; (b) the 'backward rectangular rule'; and (c) Tustin's met hod (the 'trapezoidal rule'). Thus, the normally cumbersome method of substitution for s by a rational approximation for e(sDELTA), where DE LTA is the sampling interval, followed by algebraic sorting of the z- or s-domain polynomials, is completely circumvented by the methods des cribed. Examples are given to show the simplicity and efficacy of the methods.