Computer Implementation of Wavelet Decomposition of Signal Averaged Electrocardiograms

Simple spectral analysis of signal averaged electrocardiograms (SAECG) has been the subject of numerous studies. However, the approaches reported so far appear inferior to the gold-standard time-domain analysis of SAECG. At the same time, the limitations of the time-domain analysis are well known and suggest that more complex spectral analysis of SAECG will be of clinical importance. One of the possibilities for more complex spectral analysis of SAECG is the so called Wavelet Analysis (WA) which is time-scale technique suitable for the detection of small transient signals even if they are hidden in large waves. It is obtained by expanding the signal on set of functions resulting from translation (time) and dilatation (scale) of so-called “analysing wavelet”. W provides bidimensional representation of the signal in function of time and scale. In order to apply W to SAECG, special software package written in Borland Pascal has been developed. The W of the signal s(t) is computed according to the formul where parameter corresponds to the dilatation and parameter b to the time shift. The package uses the Morlet wavelet g(t) = exp(iωt) exp(−t2/2) for ω = 5.3. Empirically, 54 scales were chosen, defined by the scale parameter = 40 × 2−m, with m ranging from 0.95 to 3.6 with an increment of 0.05. The middle frequencies of the corresponding wavelets range from 250 to 40 Hz. The package processes SAECG files in the standard ART format. To synthesise the information contained within all three wavelet transforms, wavelet vector magnitude is obtained from the wavelets of three averaged X, Y, Z leads and computed as WM = (WX2 + WY2 + WZ2)1/2. The package has been employed in several studies which showed that (a) W of SAECG is highly reproducible and (b) selected parameters of W are superior to the time-domain analysis of SAECG when used for identification of survivors of acute myocardial infarction who are at high risk of sudden death and/or ventricular tachycardia. This comparison of W and time domain analysis of SAECG used receiver operator and positive predictive characteristics which showed highly significant differences.