On the Representation of Electrocardiograms

In dealing with the sophisticated statistical analysis of medical signals such as the electrocardiogram (ECG), the first problem one encounters is how to describe each ECG by a few numbers. This is the problem of efficient representation of signals, i.e., to approximate the signal with the smallest number of basis signals while preserving the accuracy of the approximation. This paper begins with a discussion of signal representation in general. The concept of signal space is introduced, which is very helpful in understanding the ideas of signal representation. This portion of the material is of tutorial nature. Attention is then directed to a set of basis components which we have found to be very efficient for ECG representation. These components are the so-called orthonormal exponential signals. An iterative process is developed which enables us to find a set of matched exponents for the representation of all ECGs. With six pairs of such exponentials, the average error of ECG representation (QRS and T waves only, leaving out P wave) is in the vicinity of five per cent. Experimental results will be shown. Using this representation, further statistical analysis may be carried out with ease.