Page 82 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 82
CHAP. 21 LINEAR TIME-INVARIANT SYSTEMS
Combining Eqs. (2.66~) and (2.6681, we can write y(t) as
1
y(t) = -e-uIrl CY>O
2a
which is shown in Fig. 2-Sb).
2.6. Evaluate y(t) =x(t) * h(t ), where x(t) and h(t) are shown in Fig. 2-6, (a) by an
analytical technique, and (b) by a graphical method.
0 1 2 3 1
Fig. 2-6
(a) We first express x(t and h(t) in functional form:
Then, by Eq. (2.6) we have
O<r<t,t>O
Since u(7)u(t - 7) =
otherwise
u(r)u(t - 2 - 7) = (A 0<7<t-2,t>2
otherwise
3<7<t,t>3
~(7- 3)u(t - 7) =
otherwise
3<~<t-2,t>5
U(T-~)U(~-~-T)
=
otherwise
