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

TABLAS DE TRANSFORMADA Z
( )f t F. Continua
( )f kT F. Discreta,
muestreada
( )F s Transforma de
Laplace
( )F Z Transformada Z
( )t
Impulso de Dirac
( )kT 1 1
( )t T  ( )t kT  * TS
e
( )t
Escalón Unitario
( )kT
1
S 1
Z
Z 
( )t T  ( )t kT  *
TS
e
S

( )t kT T  
SkT T S
e
S
 
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  
3 2
4
( 4 1)
1
T z z z
z
 

21
2
t  
21
2
kT 3
1
S  
2
3
( 1)
2 1
T z z
z


1m
t 
;
1,2,3,...m 
( 1)!
m
m
s

1
1
10
lim ( 1)
m
Tt
m
mb
z
z e
b




                  
at
e akT
e
1
S a aT
Z
Z e

at
te akT
kTe
 
2
1
S a  
2
aT
aT
Te z
z e



2 at
t e
 
2 akT
kT e
 
3
2
S a  
2
3
( )aT aT
aT
T e z z e
z e
 



sin( )bt sin( )bkT 2 2
b
s b
2
sin( )
2 cos( ) 1
z bT
z z bT 
cos( )bt cos( )bkT 2 2
S
S b
2
2
sin( )
2 cos( ) 1
z z bT
z z bT

 
sin( )at
e bt
sin( )akT
e bkT
2 2
( )
b
S a b  2 2
sin( )
2 cos( )
aT
aT aT
ze bT
z ze bT e

 
 
cos( )at
e bt
cos( )akT
e bkT
2 2
( )
S a
S a b

 
2
2 2
cos( )
2 cos( )
aT
aT aT
z ze bT
z ze bT e

 

 

cos( )at
e t 
 cos( )akT
e kT 
 2 2
cos( )( ) sin( )
( )
S a
s a
  

 
 
2 2
cos( )( ) sin( )
( )
z z z
z
   
 
 
 
Donde:
cos( )
sin( )
aT
aT
e T
e T
 
 




1 at
e
 1 akT
e

( )
a
S S a
 
  
1
1
aT
aT
e z
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 z e z e

 
 
  
at bt
e e 
 akT bkT
e e 

( )( )
b a
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
 
 
     
 
(1 ) at
at e
 (1 ) akT
akT e
 2
( )
S
S a  
2
(1 ) aT
aT
z aT e z
z e


    

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
  

       
 
bT at
e e
a b
 


1
( )( )S a S b 
1
bT aT
z z
a b z e z e 
 
 
    
1
(1 )aT
e
a


1
( )S S a  
1 (1 )
( 1)
aT
aT
e z
a z z e


 
 
 
   
1 1
( )
aT
e
t
a a


 2
1
( )S S a  2
1 (1 )
( 1) ( 1)
aT
aT
Tz e z
a z a z z e


 
  
    
k
a
z
z a
1k
a 
1k 
1
z a
1k
ka 
 
2
z
z a
2 1k
k a 
 
3
( )z z a
z a


3 1k
k a 
 
2 2
4
( 4 )z z az a
z a
 

 
k
a
z
z a

cos( )k
a k
z
z a
2
( 1) k
k k a 

 
3
2z
z a
( 1)...( 2)k k k m  
( 1)!
( 1)m
z m
z


21
( 1)
2
k
k k a 
 3
( )
z
z a

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

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