MEEN 651 Control System Design Dr . Alexander G . Parlos

The complex exponential signal is given by x(t) = C e, (1) where C and a are, in general, complex numbers. If these are real numbers, then x(t) is called a real exponential and depending on the sign of a it can become either a growing exponential (a > 0) or a decaying exponential (a < 0). If a = 0 then x(t) is the constant C. An equally important class of complex exponential signals is obtained when a is purely imaginary. In this case, we obtain x(t) = e0. (2) An important property of this signal is that it is periodic. A class of signals closely related to the complex exponential is the sinusoidal signal x(t) = Acos(ω0t+ φ), (3) where it is common to write ω0 = 2πf0, where f0 has the units of cycles per second or Hertz (Hz). The fundamental period of the sinusoid is given by