Digital Simulation of LTI Analog Systems

This Chapter is devoted to relations between the s-domain and the z-domain. First, we develop the formula relating the one-sided Laplace transform and the one-sided \( \mathcal{Z} \) -transform and define the transformation called bilinear. Then we introduce the notion of the digital simulator of an analog system and present some methods of discretization of ordinary differential equations. Two methods of design of IIR filters will be presented: the impulse invariance method and the bilinear transformation method. This chapter recapitalizes the theory of LTI systems presented in Chaps. 3 , 4 , 5 , 6 and 7 .