Digital Signal Processing Reference
In-Depth Information
the noisy signal
y
(
t
). Verify that the output of the filter is predomi-
nantly the 3 KHz signal.
•
Digital low-pass filter
Design a digital low-pass filter with cutoff frequency of 4 KHz, to
filter out the sinusoidal signal
s
(
t
) from the noisy signal
y
(
t
). As in
the bandpass case, verify that the output of the filter is predomi-
nantly the 3 KHz signal.
Repeat the simulation, using both digital bandpass filtering and digital low-
pass filtering, for different noise levels, with SNR (voltage) of 20 dB and
10 dB, respectively.
6.3.4
Filtering of Noisy Video Signals
Exercise 5: Filtering of two-dimensional spatial signals mixed with random
noise
A 2-d digital picture
1
representing the letter
E
is transmitted through the
system shown in
Figure 6.3
.
Stage 1. Image Degradation
a.
Obtain a 16
16 picture matrix
x
(
n
1
, n
2) consisting of 256 pixels,
representing the letter
E
, with each pixel quantized to only 2 levels,
×
0 or 1. Please refer to
Figure 6.1
,
which shows how to represent the
letter
E
in pixel format.
b.
16 transmission matrix
h
(
n
1
, n
2) by sampling the
following continuous function:
Obtain the 16
×
222
−
jkxyz
+
+
e
xyz
hxy
(, )
=
(6.16)
2
2
2
++
where the propagation constant
k
= 1 m
-1
and the propagation dis-
tance
z
= 5 m. Sample the function in the interval -8 m
≤
x
≤
7 m,
-8 m
≤
y
≤
7 m (i.e.,
∆
x
= 1m and
∆
y
=1m, if we have a 16
×
16
matrix). All spatial variables are defined in meters (m).
c.
Obtain the degraded image matrix
y
(
n
1
, n
2
)
= x
(
n
1
, n
2
)
** h
(
n
1
, n
2
)
+
η
16
random noise matrix
having a
maximum value of 0.2. The random noise matrix is generated by the
MATLAB command
>> M *rand(N);
M
is the maximum value of the noise and
N
is the order of the noise matrix
(
N
= 16, in our case)
(
n
1
, n
2
), where
η
(
n
1
, n
2
) is a 16
×
