Tabla de Dualidad Transformada Z, Transformada de LaPlace y Discreta.

Tabla completa de equivalencia de funciones en el tiempo, tiempo discreto y frecuencia, equivalencia entre tranformada de laplace, transformada Z.

1. TABLAS DE TRANSFORMADA Z ()ft
F. Continua ()f kT
F. Discreta,
muestreada ()Fs
Transforma de
Laplace ()FZ
Transformada Z ()td

Impulso de Dirac ()kTd
1 1 ()tTd-
()t kTd- * TS
e
- ()tu

Escalón Unitario ()kTu
1
S 1
Z
Z- ()tTu-
()t kTu- * TS
e
S
-
()t kT Tuw-- SkT T S
e
S
w-- t

Rampa kT
2
1
S 2
( 1)
Tz
z-
2
t
()
2
kT
3
2
S ()
2
3
( 1)
1
T z z
z
+
-
3
t
()
3
kT
4
6
S ()
32
4
( 4 1)
1
T z z z
z
++
- 21
2
t
()
21
2
kT 3
1
S ()
2
3
( 1)
21
T z z
z
+
- 1m
t
-
;1,2,3,...m=

( 1)!
m
m
s
- 1
1
1
0
lim ( 1)
m
Tt
m
m
b
z
ze
b
-
-
-
-
®
éù æö
÷çêú ¶ ÷ç ÷êú ç - ÷ç ÷-êú ç ÷
ç ÷¶êú
ç ÷
÷çêú ÷çèøêúëû at
e
-
akT
e
- 1
Sa+ aT
Z
Ze
-
- at
te
-
akT
kTe
- ()
2
1
Sa+
( )
2
aT
aT
Te z
ze
-
-
- 2at
te
-
()
2
akT
kT e
- ()
3
2
Sa+
( )
2
3
()
aT aT
aT
T e z z e
ze
--
-
+
- sin( )bt
sin( )bkT 22
b
sb+ 2
sin( )
2 cos( ) 1
z bT
z z bT-+ cos( )bt
cos( )bkT 22
S
Sb+ 2
2
sin( )
2 cos( ) 1
z z bT
z z bT
-
-+ sin( )
at
e bt
-
sin( )
akT
e bkT
- 22
()
b
S a b++ 22
sin( )
2 cos( )
aT
aT aT
ze bT
z ze bT e
-
--
-+ cos( )
at
e bt
-
cos( )
akT
e bkT
- 22
()
Sa
S a b
+
++ 2
22
cos( )
2 cos( )
aT
aT aT
z ze bT
z ze bT e
-
--
-
-+

2. cos( )
at
et wq
-
- cos( )
akT
e kTwq
-
- 22
cos( )( ) sin( )
()
Sa
sa
q w q
w
++
++ 22
cos( )( ) sin( )
()
z z z
z
q a b q
ab
--
-+

Donde: cos( )
sin( )
aT
aT
eT
eT
aw
bw
-
-
=
=
1
at
e
-
-
1
akT
e
-
- ()
a
S S a+ ()
()( )
1
1
aT
aT
ez
z z e
-
-
-
-- 1 (1 )
at
at e
-
-+
1 (1 )
akT
akT e
-
-+ 2
2
()
a
S S a+ ( )
1
1
aT
aT aT
z ate
z ze ze
-
- -
--
- - - at bt
ee
--
-
akT bkT
ee
--
- ( )( )
ba
S a S b
-
++ ()
( )( )
aT bT
aT bT
e e z
z e z e
--
--
-
-- bt at
be ae
--
-
bkT akT
be ae
--
- ()
( )( )
b a S
S a S b
-
++ ( ) ( )
( )( )
aT bT
aT bT
b a z be ae z
z e z e
--
--
éù- - -
êúëû
-- (1 )
at
at e
-
-
(1 )
akT
akT e
-
- 2
()
S
Sa+ ( )
2
(1 )
aT
aT
z aT e z
ze
-
-
éù-+
êúëû
- 1
at
at e
-
-+
1
akT
akT e
-
-+ 2
()
a
S a S+ ( )
2
( 1 ) (1 )
( 1)
aT aT aT
aT
aT e z e aTe z
z z e
- - -
-
éù- + + - -
êúëû
-- bT at
ee
ab
--
-
-
1
( )( )S a S b++ 1
bT aT
zz
abz e z e
--
éù
êú -
êú- --ëû 1
(1 )
aT
e
a
-
-
1
()S S a+ ( )
1 (1 )
( 1)
aT
aT
ez
az z e
-
-
éù
-êú
êú
--êú
ëû 11
()
aT
e
t
aa
-
-
-
2
1
()S S a+ ( )
2
1 (1 )
( 1) ( 1)
aT
aT
Tz e z
az a z z e
-
-
éù
-êú
-
êú
- --êú
ëû
k
a z
za-
1k
a
-
1k³

1
za-
1k
ka
- ()
2
z
za-

21k
ka
- ()
3
()z z a
za
+
-

31k
ka
- ()
22
4
( 4 )z z az a
za
++
-
()
k
a- z
za+

3. cos( )
k
ak p z
za+
2
( 1)
k
k k a
-
- ()
3
2z
za+

( 1)...( 2)k k k m- - + ( 1)!
( 1)
m
zm
z
-
-
21
( 1)
2
k
k k a
-
- 3
()
z
za-