Page 45 - Schaum's Outline of Theory and Problems of Signals and Systems

SIGNALS AND SYSTEMS [CHAP. 1

Thus, x(t) is an energy signal.
(b) The sinusoidal signal x(t) is periodic with To = 27r/oo. Then by the result from
Prob. 1.18, the average power of x(t ) is

Thus, x(t) is a power signal. Note that periodic signals are, in general, power signals.

Thus, x(t) is neither an energy signal nor a power signal.
(d) By definition (1.16) and using Eq. (1.91), we obtain

Thus, x[nl is an energy signal.
(e) By definition (1.17)
1 N
P= lim --- C lxb1I2
N+% 2N+ 1 ,=-N
1 1
= lim - = lim (N+l)=-<a
1
N+C= 2N+ 1 ,,=,, ~ + m 2
2N+ 1
Thus, x[n] is a power signal.
(f Since Ix[n]l= I2eiJnI = 2IeJ3"l = 2,

1 N 1
N-m 2N + 1 .=
P = lim --- C lx[n]12= lim -
2'
N-+= 2N + l n= -N -N
1
= lim - 1) =4<m
4(2N+
~ + m 2N+ 1
Thus, x[n] is a power signal.

BASIC SIGNALS

1.21. Show that