Page 20 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SIGNALS AND SYSTEMS

Then the unit step function u(t) can be expressed as

(t) = S(r) di (1.31)
- m
Note that the unit step function u(t) is discontinuous at t = 0; therefore, the derivative of
u(t) as shown in Eq. (1.30) is not the derivative of a function in the ordinary sense and
should be considered a generalized derivative in the sense of a generalized function. From
Eq. (1.31) we see that u(t) is undefined at t = 0 and

by Eq. (1.21) with $(t) = 1. This result is consistent with the definition (1.18) of u(t).

C. Complex Exponential Signals:
The complex exponential signal

Fig. 1-7 (a) Exponentially increasing sinusoidal signal; (b) exponentially decreasing sinusoidal signal.