Laplace Transformation in Continuous-Time LTI Systems

In this chapter, we deal with the one-sided Laplace transformation, widely applied in analog systems. We recall in brief the definition and basic properties of the Laplace transformation. We prove its usefulness in solving differential input-output equations of LTI systems. The concepts of zero-input and zero-state responses are also presented. Next, using the convolution theorem, we introduce a notion of the transfer function of an analog system and present formulas for transfer functions of different system interconnections introduced in Chap. 3 . We also show the relation between the transfer function and the frequency response function of a system defined in Chap. 4 . A special section is dedicated to elements of the theory of stability of analog systems. In the last section, we present in detail three classes of real filters: Butterworth and Chebyshev (type I and II), with their transfer functions and magnitude responses.