Digital Signal Processing Reference
In-Depth Information
Filtered
output at
frequency
f
0
Hz
Bandpass
filter with
center
frequency
f
0
Hz
Signal
s(t)
+
Noise
n(t)
(
FIGURE 8.3
Signal filtering from a combination of signal and noise.
additive noise
n
(
t
), which adds on to the transmitted signal
s
(
t
) at a frequency
of
f
0
Hz. Several methods have been developed to tackle the problem of noise
removal from the corrupted signal
y
(
t
)
= s
(
t
)
+ n
(
t
). The commonly used
methods include autocorrelation, and filtering.
Step 1: Design of bandpass filter using MATLAB
The filter design procedure is very similar to the bandstop filter design in
the previous application in Section 8.2. However, the steps are retraced for
convenience.
•
), convert to the
corresponding digital frequency
H
d
(
e
j
ω
), using the transformation
ω
Given the desired analog frequency response,
H
d
(
j
Ω
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.
In this application, we have to design a bandpass filter with a
center frequency of
f
1
Hz and a bandwidth of
=
Ω
f
Hz. Hence, the cutoff
frequencies of the desired bandpass filter are
f
l
=
f
1
−∆
∆
f/
2 (lower cutoff
frequency) and
f
u
=
f
1
+∆
f/
2 (upper cutoff frequency).
•
Obtain the desired
Nth
order FIR digital filter coefficients
h
(
n
), 0
≤
N
using MATLAB. The various MATLAB commands for FIR
digital filter design are given in Section 5.3.2 of this topic. Examples
of these commands are
fir1
,
fir2
, and
Remez
, in which the appropri-
ate windowing function should also be specified. A sample program
using the
fir1
command is given below:
n
≤
% MATLAB Program to calculate the FIR bandpass filter
coefficients
N = 50
; specifies the filter order (50)
fs = 8000
; specifies the sampling frequency (8 KHz)
f =[
f
l
f
h
]
; specifies the analog filter cutoff
frequency vector in Hz.
