SIGNALS AND SYSTEMS
CHAP. 11
Determine the even and odd components of the following signals:
Am.
(a) xe(t) = i , xo(t) = i sgn t 1 (b) x,(t) = -cos wot, xJt)
fi
=
1 -sin
fi
wot
(c) x,[nl = jcos n,n, xo[nl = -sin Ron ( d l 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.
(
( a ) x(r) = cos 2r
1)
+-
( 1 ("4") (2+ . ( y)
( g ) x[nl=cos - cos (h) x[n] = cos Am.
sln
( a ) Periodic, period = .rr
(c) Nonperiodic (el Nonperiodic ( g ) Nonperiodic
- 2cos(?) (b) (dl (f (h)
Periodic, period Periodic, period Periodic, period Periodic, period
= .rr =2 =8 =
16