The table below provides a number of unilateral and bilateral
ztransforms. The table also
specifies the region of
convergence.
The notation for z
z found in the table below may differ from that found
in other tables. For example, the basic ztransform of
un
u
n
can be written as either of the following two
expressions, which are equivalent:
zz−1=11−z1
z
z
1
1
1
z
1
(1)
Table 1
Signal 
ZTransform 
ROC 
δn−k
δ
n
k

z−k
z
k

Allz
All
z

un
u
n

zz−1
z
z
1

z>1
z
1

−u(−n)−1
u
n
1

zz−1
z
z
1

z<1
z
1

nun
n
u
n

zz−12
z
z
1
2

z>1
z
1

n2un
n
2
u
n

z(z+1)z−13
z
z
1
z
1
3

z>1
z
1

n3un
n
3
u
n

z(z2+4z+1)z−14
z
z
2
4
z
1
z
1
4

z>1
z
1

(−αn)u(−n)−1
α
n
u
n
1

zz−α
z
z
α

z<α
z
α

αnun
α
n
u
n

zz−α
z
z
α

z>α
z
α

nαnun
n
α
n
u
n

αzz−α2
α
z
z
α
2

z>α
z
α

n2αnun
n
2
α
n
u
n

αz(z+α)z−α3
α
z
z
α
z
α
3

z>α
z
α

∏
k
=1mn−k+1αmm!αnun
k
1
m
n
k
1
α
m
m
α
n
u
n

zz−αm+1
z
z
α
m
1

γncosαnun
γ
n
α
n
u
n

z(z−γcosα)z2−(2γcosα)z+γ2
z
z
γ
α
z
2
2
γ
α
z
γ
2

z>γ
z
γ

γnsinαnun
γ
n
α
n
u
n

zγsinαz2−(2γcosα)z+γ2
z
γ
α
z
2
2
γ
α
z
γ
2

z>γ
z
γ
