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

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

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

Figure 3.12

Figure 3.13

Figure 3.14

Measured ECG = ECG without interference + interference

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

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