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 * TSe ( )t

Escalón Unitario ( )kT 1

S

1Z

Z

( )t T ( )t kT * TSe

S

( )t kT T SkT T Se

S

t Rampa kT 2

1S

2( 1)Tz

z

2t 2kT 3

2S

2

3

( 1)1

T z zz

3t

3kT 4

6S

3 2

4

( 4 1)1

T z z zz

212

t 212

kT 3

1S

2

3

( 1)2 1

T z zz

1mt ;1, 2,3,...m

( 1)!m

ms

1

110

lim ( 1)

mTt

mmb

zz eb

ate akTe 1

S a

aT

ZZ e

atte akTkTe 2

1S a

2

aT

aT

Te z

z e

2 att e 2 akTkT e 3

2S a

2

3

( )aT aT

aT

T e z z e

z e

sin( )bt sin( )bkT 2 2

bs b

2

sin( )2 cos( ) 1z bT

z z bT

cos( )bt cos( )bkT 2 2

SS b

2

2

sin( )2 cos( ) 1

z z bTz z bT

sin( )ate bt sin( )akTe bkT 2 2( )b

S a b

2 2

sin( )2 cos( )

aT

aT aT

ze bTz ze bT e

cos( )ate bt cos( )akTe bkT 2 2( )S a

S a b

2

2 2

cos( )2 cos( )

aT

aT aT

z ze bTz ze bT e

cos( )ate t cos( )akTe kT 2 2

cos( )( ) sin( )( )

S as a

2 2

cos( )( ) sin( )( )

z z zz

Donde: cos( )sin( )

aT

aT

e Te T

1 ate 1 akTe ( )a

S S a

1

1

aT

aT

e z

z z e

1 (1 ) atat e 1 (1 ) akTakT e 2

2( )a

S S a

11

aT

aT aT

z atez z e z e

at bte e akT bkTe e ( )( )b a

S a S b

( )( )( )

aT bT

aT bT

e e zz e z e

bt atbe ae bkT akTbe ae

( )( )b a S

S a S b

( ) ( )

( )( )

aT bT

aT bT

b a z be ae z

z e z e

(1 ) atat e (1 ) akTakT e 2( )S

S a

2

(1 ) aT

aT

z aT e z

z e

1 atat e 1 akTakT e 2

( )a

S a S

2

( 1 ) (1 )

( 1)

aT aT aT

aT

aT e z e aTe z

z z e

bT ate ea b

1

( )( )S a S b 1

bT aT

z za b z e z e

1 (1 )aTea

1

( )S S a

1 (1 )

( 1)

aT

aT

e za z z e

1 1( )aTet

a a

2

1( )S S a

2

1 (1 )( 1) ( 1)

aT

aT

Tz e za z a z z e

ka z

z a

1ka 1k

1

z a

1kka 2

zz a

2 1kk a 3

( )z z az a

3 1kk a

2 2

4

( 4 )z z az az a

ka z

z a

cos( )ka k z

z a

2( 1) kk k a 3

2zz a

( 1)...( 2)k k k m ( 1)!

( 1)m

z mz

21 ( 1)2

kk k a 3( )z

z a