Digital Signal Processing Reference
In-Depth Information
wn
1
()
wn
2
()
0 51
08
.
yn
1
()
x
()
0373
0
.
y
()
1
z
1
z
07460
.
04129
.
0 5654
.
1
0215
.
1
z
1
z
05108
.
03730
.
00790
.
04776
.
FIGURE 8.40
Cascade realization of IIR filter in Example 8.23 in direct-form II.
The difference equations for the implementation of the first section are
w
1
ðnÞ¼xðnÞ0:5654w
1
ðn 1Þ0:4776w
1
ðn 2Þ
y
1
ðnÞ ¼ 0:5108w
1
ðnÞ þ 1:0215w
1
ðn 1Þ þ 0:5108w
1
ðn 2Þ
The difference equations for the implementation of the second section are
w
2
ðnÞ¼y
1
ðnÞ0:4129w
2
ðn 1Þ0:0790w
2
ðn 2Þ
yðnÞ¼0:3730w
2
ðnÞþ0:7460w
2
ðn 1Þþ0:3730w
2
ðn 2Þ
Note that for both direct-form I and direct-form II, the output from the first filter section becomes the input for the
second filter section.
8.9
APPLICATION: 60-HZ HUM ELIMINATOR AND HEART RATE DETECTION
USING ELECTROCARDIOGRAPHY
Hum noise created by poor power suppliers, transformers, or electromagnetic interference sourced by
a main power supply is characterized by a frequency of 60 Hz and its harmonics. If this noise interferes
with a desired audio or biomedical signal (e.g., in electrocardiography [ECG]), the desired signal could
be corrupted. The corrupted signal is useless without signal processing. It is sufficient to eliminate the
60-Hz hum frequency with its second and third harmonics in most practical applications. We can
complete this by cascading with notch filters having notch frequencies of 60 Hz, 120 Hz, and 180 Hz,
respectively.
Figure 8.41
depicts the functional block diagram.
Now let us apply the 60-Hz hum eliminator to an ECG recording system. ECG is a small electrical
signal captured from an ECG sensor. The ECG signal is produced by the activity of the human heart, thus
it can be used for heart rate detection, fetal monitoring, and diagnostic purposes. The single pulse of the
ECG is depicted in
Figure 8.42
, which shows that the ECG signal is characterized by five peaks and
valleys, labeled P, Q, R, S, and T. The highest positive wave is the R wave. Shortly before and after the R
wave are negative waves called the Q wave and S wave. The P wave comes before the Q wave, while the
T wave comes after the S wave. The Q, R, and S waves together are called the QRS complex.
The properties of the QRS complex, with its rate of occurrence and times, heights, and widths,
provide information to cardiologists concerning various pathological conditions of the heart. The
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