ABSTRACT
The Laplace transform is a useful analytical tool for converting time-domain signal descriptions into functions of a complex variable. This complex domain description of a signal provides new insight into the analysis of signals and systems. In addition, the Laplace transform method often simplifies the calculations involved in obtaining system response signals. The Laplace transform completely characterizes the exponential response of a time-invariant linear function. This transformation is formally generated through the process of multiplying the linear characteristic signal x(t) by the signal e-st and then integrating that product over the time interval. In evaluating the Laplace transform integral that corresponds to a given signal, it is generally found that this integral will exist for only a restricted set of s values. Frequency-domain differentiation formulas may be obtained by differentiating the Laplace transform with respect to s.
