3.3.1 synchronized averaging. problem propose a time-domain technique to remove random noise given...
TRANSCRIPT
3.3.1 Synchronized averaging
Problem
• Propose a time-domain technique to remove random noise given the possibility of acquiring multiple realizations of the signal or event of interest
Solution
• Linear filters fail to perform when the signal and noise spectra overlap.
• Synchronized signal averaging can separate a repetitive signal from noise without distorting the signal
• ECG signals may be filtered by detecting the QRS complexes and using their positions to align the waveforms for synchronized averaging
)()()( nnxny kkk
NnnM
nxM
nyM
M
kk
M
kk
M
kk ,...,2,1;)(
1)(
1)(
1
111
)(nxk
)(nxk
)(nk
represents the kth observation of the original uncorrupted signal
represents the noise in the kth copy of the observed signal
Synchronized average:
21
0
21
0
1
0
])([])([
])(][)([)(
yknyxnx
yknyxnxk
N
n
N
n
N
nxy
X is the template
Y is the ECG signal
x yand are the average of the corresponding signals
Figure 3.12
Figure 3.13
Figure 3.14
12
1
12
1
12
1
121212
222
111
12
1
12
1
12
1
)()(
(n),)(
12~1 ,
kk
kk
kk
ji
ji
kkk
nnxny
nnxny
nxnx
j in
nnxny
nnxny
knnxny
Measured ECG = ECG without interference + interference
average edsynchroniz theof variance theis andmean, theis where},,{
}12
,{}12
,{
}1212
1,0{}0,12
12
1{
}12,0{12
1}0,12{
12
1
12,012
10,12
12
1
0. is and small, very is because ,
12,01212
1012,12
12
1
. and are so andt independenmutually are and because ,
12,1212
112,12
12
1
12
1
12
1
12
1
22
22
22
22
2
22
22
12
1
12
1
12
1
ssss
xx
x
x
x
x
x
jiji
xx
kk
kk
kk
ηηxx
nnxny
For synchronized averaging of order M
The resultant signal has a mean close to x
and a variance equal to
(a standard deviation equal to
Advantage
No spectral content of the signal is lost !