Biomedical Engineering Reference
In-Depth Information
(Equation 4.2) can be used subject to the following constraint:
X
(
n
)=
|X
(
n
)
|
if
|X
(
n
)
| >θ
(4.3)
θ
if
|
X
(
n
)
|≤
θ
The second derivative (Ahlstrom and Thompkins, 1983) can also be com-
puted as
y
(
n
)=
X
(
n
+2)
2) (4.4)
Some algorithms also use linear combinations of the first and second deriva-
tives (Balda, 1977), for example,
−
2
X
(
n
)
−
X
(
n
−
y
(
n
)
y
(
n
)
z
(
n
)=1
.
3
|
|
+1
.
1
|
|
(4.5)
4.6.1.2 Digital Filter Algorithms
Some QRS-detection algorithms are based on enhancing certain portions of
the waveform through bandpass filtering (Okada, 1979; Dokur et al., 1997;
Fancott and Wong, 1980; Suppappola and Sun, 1994; Sun and Suppappola,
1992). A simple method (Okada, 1979) is to bandpass filter the ECG signal
and process it using a nonlinear function
y
2
(
n
)=
y
1
(
n
)
k
=
m
y
1
(
n
+
k
)
2
(4.6)
k
=
−m
where
y
1
(
n
) is the filtered ECG signal. Multiplication of backward difference
(MOBD) algorithms (Suppappola and Sun, 1994; Sun and Suppappola, 1992)
use products of adjacent sample derivatives to obtain the QRS feature
k
=1
|
N
y
1
(
n
)=
X
(
n
−
k
)
−
X
(
n
−
k
−
1)
|
(4.7)
where
N
defines the order of the model. Additional constraints can be imposed
on the signal to avoid the effects of noise. Other algorithms (Hamilton and
Thompkins, 1986) have utilized threshold values on the bandpass filtered sig-
nal. QRS peaks are detected by comparing amplitudes with a variable
v
,
where
v
is the most recent maximum sample value. If, for example, the fol-
lowing ECG samples fall below
v
/2, a peak is detected. It is also possible
to use recursive and nonrecursive median filters (Yu et al., 1985) based on
the assumption that the QRS peaks occur within the passband of the filters.
These filters have the following form:
y
(
n
) = median[
y
(
n
−
m
)
,...,y
(
n
−
1)
,X
(
n
)
,X
(
n
+1)
,...,X
(
n
+
m
)]
(4.8a)
y
(
n
) = median[
X
(
n
−
m
)
,...,X
(
n
−
1)
,X
(
n
)
,X
(
n
+1)
,...,X
(
n
+
m
)]
(4.8b)
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