2
ii)
Design a 10
th
order Hamming windowed FIR low-pass filter with cut-
off frequency at 1000 Hz if the sampling frequency is 8000 Hz. Hence,
find an expression for the multipliers
a
(
k
),
k
= 0, 1, 2,…10 of the
designed filter.
8
iii)
How would you use these values to design a high-pass filter with cut-
off at 1000 Hz. Explain your answer.
3
Total
25
1;
(
)
0;
c
j
LP
c
H
e
)
(
)
sin(
]
[
c
c
c
LP
n
n
n
h

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ELEC309
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Table of z-Transforms
The z-transform of a discrete-time signal
n
f
is defined as:
n
n
z
n
f
z
F
Note that
n
u
is the unit step defined as:
,
0
for
1
and
,
0
for
0
n
n
n
u
and that
n
is the unit impulse defined as:
0
for
1
and
,
0
for
0
n
n
n
n
f
z
F
1
n
1
2
a
n
a
z
3
n
u
1
/
z
z
4
n
u
a
n
a
z
z
/
5
n
f
z
F
6
a
n
f
z
F
z
a
7
n
f
a
n
a
z
F
/
8
sin
(
an
)
u
(
n
)
sin
(
a
)
z
-1
/(1-2
cos
(
a
)
z
-1
+ z
-2
)
Note:
)
sin(
)
cos(
t
j
t
e
t
j
)
sin(
)
cos(
t
j
t
e
t
j

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- Summer '19
- Digital Signal Processing, Dr A. Al-Ataby