Page 17 - Schaum's Outline of Theory and Problems of Signals and Systems

6 SIGNALS AND SYSTEMS [CHAP. 1

The normalized average power P of x[n] is defined as
1
P = lim -
N+- 2N + 1 ,,= -N
Based on definitions (1.14) to (1.17), the following classes of signals are defined:

1. x(t) (or x[n]) is said to be an energy signal (or sequence) if and only if 0 < E < m, and
so P = 0.
2. x(t) (or x[n]) is said to be a power signal (or sequence) if and only if 0 < P < m, thus
implying that E = m.
3. Signals that satisfy neither property are referred to as neither energy signals nor power
signals.
Note that a periodic signal is a power signal if its energy content per period is finite, and
then the average power of this signal need only be calculated over a period (Prob. 1.18).

1.3 BASIC CONTINUOUS-TIME SIGNALS
A. The Unit Step Function:
The unit step function u(t), also known as the Heaciside unit function, is defined as

which is shown in Fig. 1-4(a). Note that it is discontinuous at t = 0 and that the value at
t = 0 is undefined. Similarly, the shifted unit step function u(t - to) is defined as

which is shown in Fig. 1-4(b).

(a) (b)
Fig. 1-4 (a) Unit step function; (b) shifted unit step function.

B. The Unit Impulse Function:
The unit impulse function 6(t), also known as the Dirac delta function, plays a central
role in system analysis. Traditionally, 6(t) is often defined as the limit of a suitably chosen
conventional function having unity area over an infinitesimal time interval as shown in