On the Equivalence between Integer- and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, interrelations between defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions continuous discrete transfer functions. Simple transformations presented allow interconversions both systems, recovering obtained with impulse invariant method. These also used formulate a covariance equivalence. spectral correspondence implied bilinear (Tustin) transformation study two types systems. general fractional CT/DT ARMA studied considering DT (FARMA) based on nabla/delta derivatives. considered, paying special attention