tabella trasformata di laplace
TRANSCRIPT
h t( )
Laplace f t{ ( )} Trasformata Zf t( )
1
s
z
z− 1
t12s
Tz
z( )−1 2
t2
2T z z
z
2
31
2 1
( )
( )
+−
13s
tk−1 ( )!k
sk−1
lim ( )a
kk
k aTa
z
z e→−
−
− −− ∂∂ −
�
! "
$#0
11
11
e at−
te at−
1s a+
12( )s a+
z
z e aT− −
Tze
z e
aT
aT
−
−−( )2
t ek at−
1− −e at
tea
at− − −1
1 1− + −( )at e at
e eat bt− −−
sin( )at
cos( )at
k
s a k!
( )+ +1
a
s s a( )+
a
s s a2( )+
a
s s a
2
2( )+
b a
s b s a−
+ +( )( )
a
s a2 2+s
s a2 2+
( )− ∂∂ −
�
! "
$#−1 kk
k aTa
z
z e
z e
z z e
aT
aT( )
( )( )
1
1
−− −
−
−
z aT e z e aTe
a z z e
aT aT aT
aT[( ) ( ]
( ) ( )
)− + + − −− −
− − −
−1 1
1 2
z
z
z
z e
aTe z
z eaT
aT
aT−−
−−
−−
−
−1 2( )
( )
( )( )
e e z
z e z e
aT bT
aT bT
− −
− −−
− −
z aT
z z aT
sin( )
cos( )2 2 1− +z z aT
z z aT
( cos( ))
cos( )
−− +2 2 1
e btat− cos( )
e btat− sin( )
1
ab
e
a a b
e
b b a
at
bt
+−
+
+−
−
−( )
( )
1− +
+
−e bt
a
bbt
at(cos( )
sin( ))
b
s a b( )+ +2 2
s a
s a b
++ +( )2 2
b a
s s a b
2 2
2 2+
+ +( )
1s s a s b( )( )+ +
ze bT
z ze bT e
aT
aT aT
−
− −− +sin( )
cos( )2 22
z ze bT
z ze bT e
aT
aT aT
2
2 22
−− +
−
− −cos( )
cos( )( )
( )( cos( ) )
Az B z
z z ze bT eaT aT+
− − +− −1 22 2
A e bTa
bbTaT= − +−1 (cos( ) sin( )
B e ea
bbT bTaT aT= + −− −2 ( sin( ) cos( ))
)
( )
( )( ( ))Az B z
z z e z eaT bT+
− − −− −1