Digital Signal Processing Reference
In-Depth Information
8.2
Filtering Application to Extract Sinusoidal Signal
from a Combination of Two Sinusoidal Signals
Exercise 1: This two-signal filtering application consists of a series of six
steps. Please follow the instructions carefully to successfully complete the
experiment.
In many communications applications, including wireless and cellular, it is
often required to separate
two baseband signals
,
s
1
(
t
) and
s
2
(
t
), with different
frequencies,
f
1
Hz and
f
2
Hz, respectively. The essential filtering process is
shown in Figure 8.1, where a
bandstop filter
can be used to filter out the signal
s
1
(
t
) or
s
2
(
t
).
The procedure to implement the system, shown in Figure 8.1, is divided
into six experimental steps, with each step being very important to the
overall application.
Step 1: Design of digital bandstop filter using MATLAB
There are several ways to design digital filters using MATLAB, which were
discussed in
Chapter 5
. However, we will focus on the method that is avail-
able even on the simplest MATLAB student version. Real-time digital filters
can be implemented using the following protocol:
•
Given a desired analog frequency response,
H
d
(
j
), convert the latter
response to the corresponding digital frequency response,
H
d
(
e
j
Ω
ω
),
using the transformation
T
, where
T
(sec.) is the sampling
interval. Note that
T = 1/f
s
, where
f
s
is the sampling frequency (Hz).
The default sampling rate in the DSK is 8 KHz.
ω
=
Ω
In this application, we have to design a bandstop filter with a center
frequency of
f
1
Hz, and a bandwidth of
∆
f
Hz. Hence, the cutoff frequencies
Filtered
output at
frequency
f
2
Hz (or
f
1
Hz)
Bandstop
filter with
center
frequency
f
1
Hz (or
f
2
Hz)
Signal
s
1
(t)
+
Signal
FIGURE 8.1
Signal filtering from a combination of two signals of different frequency.
