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Department of Electrical and Computer Engineering
Digital Speech Processing
Homework No. 4
Problem 1
Consider the ﬁve
N
point ﬁnite duration windows listed below:
1. Rectangular Window
w
R
[
n
] =
(
1 0
≤
n
≤
N

1
0 otherwise
2. Triangular Window
w
T
[
n
] =
2
n/
(
N

1)
0
≤
n
≤
(
N

1)
/
2
2

2
n/
(
N

1) (
N

1)
/
2
≤
n
≤
N

1
0
otherwise
3. Hamming Window
w
H
[
n
] =
(
0
.
54

0
.
46 cos(2
πn/
(
N

1)) 0
≤
n
≤
N

1
0
otherwise
4. Hanning Window
w
H
N
[
n
] =
(
0
.
5

0
.
5 cos(2
πn/
(
N

1)) 0
≤
n
≤
N

1
0
otherwise
5. Blackman Window
w
B
[
n
] =
(
0
.
42

0
.
5 cos(2
πn/
(
N

1)) + 0
.
08 cos(4
πn/
(
N

1)) 0
≤
n
≤
N

1
0
otherwise
(a) Using Matlab, with a value of
N
= 31, make a single plot showing the
window time responses of all 5 windows over the region 0
≤
n
≤
N

1
(b) Using Matlab, again with a value of
N
= 31 and using a 1024point FFT,
calculate and make a single plot of the log magnitude responses of all 5 windows
from 0 to
F
S
/
2 (assume
F
S
= 10000). (Be sure to normalize the peak of each
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 Fall '08
 Rabiner,L

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