1. 3.3.1 Synchronized averaging

2. Problem
Propose a time-domain technique to remove random noise given the possibility of acquiring multiple realizations of the signal or event of interest

3. 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

4. represents the kth observation of the original uncorrupted signal
represents the noise in the kth copy of the observed signal
Synchronized average:

5. X is the template
Y is the ECG signal
and
are the average of the corresponding signals

6. Figure 3.12

7. Figure 3.13

9. Figure 3.14

10. Measured ECG = ECG without interference + interference

12. 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

14. No spectral content of the signal is lost !
Advantage
No spectral content of the signal is lost !