Direct mathematical method for real-time ischemic episodes detection from electrocardiograms using the discrete Hermite transform

A real-time automated identification technique is developed for the detection of ischemic episodes in long-term electrocardiographic (ECG) signals using mathematical expansions involving the Discrete Dilated Hermite Transform. The Discrete Hermite functions could be viewed as a set of orthogonal vectors that resemble a finite Fourier series. They are generated easily as eigenvectors of a symmetric tridiagonal matrix that commutes with the centered Fourier matrix. The Discrete Hermite Transform (DHmT) values are computed from a simple dot product between an individual ECG complex extracted from the European Society of Cardiology (ESC) ST-T database and the corresponding discrete Hermite function. These values are found to contain information about the ECG shape, highlighting changes between ST segment and T wave alterations which are the features of ischemic episodes. This information from the discrete Hermite transform, based on an orthonormal set of n-dimensional digital Hermite functions that serve as shape-identification functions, can be used to identify ischemic episodes from the ECG. The performance measures resulting from applying this method to detect ischemic episodes were Sensitivity 87 %, Specificity 86 %, and positive predictive accuracy 81 %. The computer time to analyze one heartbeat for ischemia with this method is 0.031 seconds on a standard PC.