82 4 Ltktplace Transform
(4.13)
(J5T + ~ 2 - I1 ( - L A Y
C { * r " " ( t ) } = sG{.r"(t)} - -
j2T)Z (27 )Z (2T)Z
As s " " ( t ) i s zcro a t d l poiiils whcrt\ it is definccl, with (4.42) and some rcasrangr- merit,
The l ~ ~ d a o e traiisforrn ol the triangltl sigiial is tliercfore
(4.45)
d X ( s )
~ = j z ( r ) (-t)c-"'dt
C{f r ( t ) } = - _ d x ( s ) cl s : s E R 0 C I r ) 1 (4 I 47)