Tabla Transformada Z

Tabla de Transformadas Zeta
Definición
∞
X
F (z) = Z x(t) = Z x(kT ) =
x(kT )z −k
k=0
Funciones más comunes
f (t)
f (k · T ) o f (k)
1
1
t
k·t
t2
(k · t)2
t3
(k · t)3
e−at
e−akT
te−at
kT e−akT
t2 e−at
(kT )2 e−akT
1
a
(1 − e−at )
1
a
1 − e−akT
at − 1 + e−at
akT − 1 + e−akT
sin ωt
sin ωkT
cos ωt
cos ωkT
e−at sin ωt
e−at sin ωkT
e−at cos ωt
e−at cos ωkT
F (s) = L {f } (s) F (z)
1
1
1−z −1
s
1
T z −1
−1 )2
2
(1−z
s
2
T 2 z −1 (1+z −1 )
(1−z −1 )3
s3
6
T 3 z −1 (1+4z −1 +z −2 )
(1−z −1 )4
s4
1
1
1−e−aT z −1
s+a
1
T e−aT z −1
2
(1−e−aT z −1 )2
(s + a)
2
T 2 e−aT (1+e−aT z −1 )z −1
3
(1−e−aT z −1 )3
(s + a)
1
1−e−aT
az(1−e−aT z −1 )(1−z −1 )
(s + a) s
a2
[(aT −1+e−aT )+(1−e−aT −aT e−aT )z−1 ]z−1
(1−e−aT z −1 )(1−z −1 )2
(s + a) s2
ω
z −1 sin ωT
1−2z −1 cos ωT +z −2
2
2
s +ω
s
1−z −1 cos ωT
1−2z −1 cos ωT +z −2
2
2
s +ω
ω
e−at z −1 sin ωT
−at z −1 cos ωT +e−2at z −2
2
1−2e
(s + a) + ω 2
s+a
1−e−at z −1 cos ωT
2
1−2e−at z −1 cos ωT +e−2at z −2
2
(s + a) + ω