DSP
DR.Noura Ali
Sheet 4
1- Find the Z-transform of the following sequences?
5
1
6
2
a- X(n) = 2 ( )𝑛 𝑢(−𝑛 − 1)+ 3 ( )2𝑛 u(n)
b-
c- X(n) = [5,3,2,1,2,3]
d- X(n) = [2,1,3,-4,1,2]
e- X(n) = [1,3,-2,0,2,4]
↑
f- X(n) = [1,2,5,6,0,1]
↑
g- X(n) = [1,2,3,4,0,1,2,3,4]
↑
h- X(n) = u(n) – u(n-4)
i- X(n) = u(2-n) -u(-2-n)
2- Using properties of Z-transform, find the Z-transform of the
following sequences?
abcde-
X(n) = u(-n+1)
X(n) = u(-n-2)
X(n) = 2𝑛 u(n-2)
X(n) = ∝𝑛−2 u(n-2)
𝜋
X(n) = n 2𝑛 sin ( 𝑛) u(n)
f- x(n) =n[
1
( )𝑛
2
2
1
u(n) * ( )𝑛 u(n)]
4
2
g- x(n) = n u(n)
h- x(n) = n u(n-1)
1
i- x(n) = n[ ( )𝑛 u(n)]
𝑛
2
j- x(n) = 2 cos (3𝑛)u(n)
1
𝜋
3
4
k- x(n) = ( )𝑛 sin ( 𝑛)u(n)
EEC 225
MTE 241
sheet 4
DSP
DR.Noura Ali
1
l- x(n) = ( )𝑛 u(-n)
3
1 𝑛
m- x(n) =( ) [𝑢(𝑛) − 𝑢(𝑛 − 8)]
2
n- x(n) = 3 22 u(-n)
o-
3- Using the z-transform to find the convolution of the following
signals?
a- X1(n) = [2,1,0,-1,3] , x2(n) = [1,-3,2]
b- X1(n) = [1,3,0,-1,3] , x2(n) = [1,-2,2]
1
1
c- X1(n) = ( )𝑛 𝑢(𝑛) , X2(n) = ( )𝑛−2 𝑢(𝑛 − 2)
2
d- X1(n) =
2n
3
u(n) , x2(n) =
3n
u(n)
4- Find the cross correlation of the following signals using the z-
transform properties?
a- X1(n) = [1,2,3,4] , x2(n) = [4,3.2.1]
b- X1(n) = [1,0,3,0] , x2(n) = [2,1.0.1]
5- Using final value theorem, find x(∞), if X(z) is given by?
a- x(z) =
𝑧+2
4(𝑧−1)(𝑧+0.7)
2𝑧+3
b-x(z) = (𝑧+1)(𝑧+3)(𝑧−1)
6- Find the Inverse Z-Transform?
a- X(z) = 1+z+z2
b- X(z) = 1-z-1+z-2+z
c- X(x) = z2-z-4+z-1-z-2 + 2z-3
EEC 225
MTE 241
sheet 4
DSP
DR.Noura Ali
d-
EEC 225
MTE 241
sheet 4