The property of linearity of Laplace transforms was already noted and made use of in earlier
sections. We look at other interesting properties of Laplace transform in this section.
15.7.1 Time-shifting Theorem
If v(t) f(t) u(t) has a Laplace transform V(s)then v
d
(t) v(t – t
d
) f(t – t
d
) u(t– t
d
) has
a Laplace transform .
The shifting operation implied in this theorem is illustrated in Fig. 15.7-1. Note that
there is a difference between f(t – t
d
) u(t) and f(t – t
d
) u(t – t
d
). Time-shifting theorem for
unilateral Laplace transform works properly for f(t – t
d
) u(t – t
d
) but not for f(t – t
d
) u(t).
This theorem ...
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