Digital Signal Processing Reference
In-Depth Information
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Frequency (Hertz)
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Frequency (Hertz)
FIGURE 8.44
Frequency responses of three cascaded notch filters.
The second-stage design using the BLT gives the bandpass filter transfer function and difference
equation:
0
:
0464
0
:
0927
z
2
þ
0
:
0464
z
4
H
4
ðzÞ¼
1
3
:
3523
z
1
þ
4
:
2557
z
2
2
:
4540
z
3
þ
0
:
5506
z
4
y
4
ðnÞ¼
0
:
046361
y
3
ðnÞ
0
:
092722
y
3
ðn
2
Þþ
0
:
046361
y
3
ðn
4
Þ
þ
03
:
352292
y
4
ðn
1
Þ
4
:
255671
y
4
ðn
2
Þþ
2
:
453965
y
4
ðn
3
Þ
0
:
550587
y
4
ðn
4
Þ
Figure 8.45
depicts the processed results at each stage. In
Figure 8.45
, plot (a) shows the initial corrupted
ECG data, which includes 60-Hz interference and its 120 and 180 Hz harmonics, along with muscle
noise. Plot (b) shows that the 60-Hz interference and its harmonics of 120 and 180 Hz have been removed.
Finally, plot (c) displays the result after the bandpass filter. As we expected, the muscle noise has been
removed; and the enhanced ECG signal is observed. AMATLAB simulation is provided in Program 8.16.
With the procssed ECG signal, a simple zero-cross algorithm can be designed to detect the heart
rate. Based on plot (c) in
Figure 8.45
,
we use a threshold value of 0.5 and continuously compare each
of two consecutive samples with the threshold. If both results are opposite, then a zero crossing is
detected. Each zero-crossing measure is given by
zero crossing
¼
jcur sign pre signj
2
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