A third important class of signals

A third important class of signals discussed in this lecture is continuoustime and discrete-time complex exponentials. In both cases the complex exponential can be expressed through Euler's relation in the form of a real and an imaginary part, both of which are sinusoidal with a phase difference of 'N/2 and with an envelope that is a real exponential. When the magnitude of the complex exponential is a constant, then the real and imaginary parts neither grow nor decay with time; in other words, they are purely sinusoidal. In this case for continuous time, the complex exponential is periodic. For discrete time the complex exponential may or may not be periodic depending on whether the sinusoidal real and imaginary components are periodic.