Page 78 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 21 LINEAR TIME-INVARIANT SYSTEMS

(b) Let x(t)* h,(t)= f,(t) and h,(t)* h2(t)= f2(t). Then

Substituting A =a - T and interchanging the order of integration, we have

Now, since

we have

Thus,

2.2. Show that

I-to
(d) x(t) * u(t - to) =
(a) By definition (2.6) and Eq. (1.22) we have

(b) By Eqs. (2.7) and (1.22) we have

(c) By Eqs. (2.6) and (1.19) we have

7<t
since u(t - 7) =
7>t'