Electric Circuits and Networks

15.2 EXPANSION OF A SIGNAL IN TERMS OF COMPLEX EXPONENTIAL FUNCTIONS

The signal 2 e^0.2t cos2t u(t) does not have a Fourier transform because it is not absolutely integrable. We now formulate the signal decomposition problem in a general form. We define the kind of signals that we are going to use first.

Let v(t) = f(t) u(t) be a right-sided function of time. We consider only right-sided functions of time in the analysis of linear time-invariant circuits since that is the kind of functions we apply to them and that is the kind of functions we get from them. The underlying function f(t) is defined for all t and may be non-zero for t < 0. For instance, if f(t) = 1 for all t then v(t) defined as f(t) u(t) is a unit step function and stands for switching ...