Magnitude/phase spectra of 7 independent EKG features.

Shown below is the result of the frequency-delay analysis of the previous page, for a filter consisting of a single sine pulse from 0-32 Hz (horizontal axis), delayed from 0-1 sec (vertical axis). At right is the same image with the scale considerably increased and all out-of-scale values pegged at their endpoint colors. This binary posterization clearly shows the presence of 7 distinct features in the input EKG signal. These features are labeled from F1 to F7 in order of increasing starting frequency. Note that some features roll from the bottom of the plot back to the top, since the input signal is periodic. Also note that the starting time for all features converges on the middle left of the plot (the leftmost tip of F1), which appears to come at a time just after the maximum value of F1 is reached. This is consistent with the hypothesis that the T "wave" of the EKG (represented in the plot by F1) indicates the repolarization of the myocardium and the start of another EKG wave cycle.

In order to analyze the spectra of each of these features independently of the others, I have reprogrammed the peak finding component to search for and trace out the path of each feature in the 2d image. Given a starting point in frequency-delay coordinates, the peak component can trace out the maximum values of the "ridge" corresponding to each feature, record the {frequency, delay, maximum} vectors along this path, and send these values to other components (such as another plot).

In the image below, the peak component has tracked the path of F2 (shown in yellow), and the 1d plot shows the maximum value along this path at all frequencies above the starting point. This set of maximum values is the spectrum magnitude of the F2 feature, independent of all other features in the signal. Note that the shape of this spectrum is that of a band-pass filter: it is zero for low frequencies, rises to a peak frequency (here at about 12 Hz), and then dies away again at higher frequencies.

The peak component can also be set to output the delay of each feature's path, and that delay can be transformed into a phase difference, which varies with frequency. The resulting magnitude and phase spectra for the first 7 features of the average V(3,3) EKG signal are as follows:

Again, note that the magnitude spectra of all features look like band-pass filters. Also, note that the phases of all features are straight lines, while their delays are curved. Each phase rate (slope of the line) is also very large, due to the substantial initial time/phase delays of each feature, which are on the order of 25-33% of the signal length for F1-2.

These results suggest that the EKG signal can be represented or decomposed as a set of ~7 or less band-pass filters. The actual EKG trace is the result of the sum of the impulse responses of each of these band-pass filters operating in parallel (i.e. relatively independently of one another). Each feature filter is parameterized by a time delay of the impulse, and also a localized frequency/time distribution of its reponse to the impulse, all of which can be implemented as a band-pass filter with linear phase.

Here is a detail of features 3-7. Note that the shapes of F1, F3, and F4 are similar, while those of F2, F5, F6, and possibly F7 also appear similar.

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