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TABLA DE TRANSFORMADAS z
X(s)

x(t)

x(kT) ó x(k)

X(z)

1

Delta Kronecker
1, k = 0
δ 0 (k ) = 
0,k ≠ 0

1

2

z-k

1
s
1
s+a
1
s2

1(t)

1, n = k
δ0(n-k)= 
0,n ≠ k
1(k)

e-at

e-akT

t

kT

62
s3

t2

(kT)2

7

6
s4

t3

(kT)3

8

a
s( s + a)

1 - e-at

1-e-akT

3
4
5

9

e-at - e-bt
b−a
( s + a)( s + b)

e-akT - e-bkT

1
( s + a) 2

te-at

s
( s + a) 2

(1-at)e-at

2
( s + a) 3

t2e-at13

a2
s2 ( s + a )

at-1+e-at

akT - 1 + e-akT

14

w
2
s + w2

sin wt

sin wkT

10

11

12

kTe-akT

1
1 − z −1
1
1 − e − aT z −1
Tz −1

(1 − z−1 ) 2
T2 z −1(1 + z −1 )
(1 − z −1 ) 3
T3z −1(1 + 4z−1 + z −2 )
(1 − z−1 ) 4
(1 − e −aT ) z −1
(1 − z −1 )(1 − e −aT z −1 )
( e −aT − e− bT ) z −1
(1 − e−aT z −1 )(1 − e − bT z −1 )
Te − aTz−1

(1 − e−aTz−1)2

(1-akT)e-akT

1 − (1 + aT) e−aT z−1

(1 −e−aTz−1) 2

Control Digital - © JAM 1998

(kT)2e-akT

1 − (1 + aT) e −aT z −1

(1 − e−aTz−1) 2
[( aT−1+e −aT ) + (1−e −aT −aTe −aT ) z −1] z −1
(1 − z −1 ) 2 (1 − e −aT z −1 )
z −1sinwT
1 − 2 z −1 cos wT +z −2

TABLA DE TRANSFORMADAS z
x(t)

x(kT) ó x(k)

15

X(s)
s
s2 + w 2

cos wt

cos wkT

16

w

e-at sin wt

e-akT sin wkT

)2

(s + a + w
17

2

s+ a

X(z)
1 − z −1 cos wT
1 − 2 z −1 cos wT + z −2e − aT z −1sinwT

1 − 2e− aT z −1 cos wT + e −2aT z −2
e-at cos wt

1 − e − aT z −1 cos wT

e-akT cos wkT

( s + a) 2 + w 2

1 − 2e− aT z −1 cos wT + e −2aT z −2

18

ak

19

k-1

1
1 − az −1
z −1

ak=1,2,3...

1 − az −1
z−1

k-1

20

ka

(1 − az−1 ) 2

(

z −1 1 + az −1

2 k-1

21

ka

(

z −1 1 + 4az−1 + a 2 z −2

k3ak-1

22

k4ak-1

23

ak cos kπ

24

(1 − az−1) 3

(

(1 − az−1)4
(1 − az−1)51

25

k (k − 1)
2!

26

k (k − 1)...(k − m + 2)
(m − 1)!

z − m +1
(1 − z −1 ) m

k (k − 1) k-2
a
2!

28

k (k − 1)...(k − m + 2) k-m+1
a
(m − 1)!

x(t) = 0, para t < 0
x(kT) = x(k) = 0, para k < 0
Amenos que se indique otra cosa, k = 0, 1, 2, 3, ...

Control Digital - © JAM 1998

)

z −1 1 + 11az−1 + 11a 2 z −2 + a 3z −3

1 + az −1
z −2
(1 − z −1 ) 3

27

)

z −2
(1 − az −1 ) 3
z − m +1
(1...