Page 64 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SIGNALS AND SYSTEMS

Determine the even and odd components of the following signals:

Am. (a) xe(t) = i, xo(t) = i sgn t
1 1
(b) x,(t) = -cos wot, xJt) = -sin wot
fi fi
(c) x,[nl = jcos n,n, xo[nl = -sin Ron
(dl xe[nl = S[nI, xo[nl = 0

Let x(t) be an arbitrary signal with even and odd parts denoted by xe(t) and xo(t),
respectively. Show that

Hint: Use the results from Prob. 1.7 and Eq. (1.77).

Let x[n] be an arbitrary sequence with even and odd parts denoted by x,[nl and xo[n],
respectively. Show that

Hinr: Use the results from Prob. 1.7 and Eq. (1.77).
Determine whether or not each of the following signals is periodic. If a signal is periodic,
determine its fundamental period.
( 1)
(a) x(r) = cos 2r + -

(1 ("4")
(g) x[nl=cos - cos -
)
+
.
-
(h) x[n] = cos (2 sln (y - 2cos(?)
Am. (a) Periodic, period = .rr (b) Periodic, period = .rr
(c) Nonperiodic (dl Periodic, period = 2
(el Nonperiodic (f Periodic, period = 8
(g ) Nonperiodic (h) Periodic, period = 16