Page 86 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 86
CHAP. 21 LINEAR TIME-INVARIANT SYSTEMS
(c)
Fig. 2-11
2.8. If x,(t) and x2(t) are both periodic signals with a common period To, the convolution
of x ,( t ) and x2(t) does not converge. In this case, we define the periodic conaolution
of x,(t) and x2(t) as
(a) Show that f(t) is periodic with period To.
(b) Show that
f (t) = la' T0x,((lx2(t - 7) d~ (2.71)
a
for any a.
(c) Compute and sketch the periodic convolution of the square-wave signal x(t)
shown in Fig. 2-12 with itself.
