OVERVIEW

Because of the linearity (superposition) property of linear time-invariant systems, we can find the response of these systems by breaking the input x( t) into several components and then summing the system response to all the components of x( t). We have already used this procedure in time-domain analysis, in which the input x( t) is broken into impulsive components. In the frequency-domain analysis developed in this chapter, we break up the input x( t) into exponentials of the form e ^st, where the parameter s is the complex frequency of the signal e ^st, as explained in Section 1.4-3. This method offers an insight into the system behavior complementary to that seen in the time-domain analysis. In fact, the time-domain and the frequency-domain methods are duals of each other.

The tool that makes it possible to represent arbitrary input x( t) in terms of exponential components is the Laplace transform, which is discussed in the following section.