An FRI Model for Asymmetric Pulse Train and Characterization of Ventricular Hypertrophy Condition

We address the problem of modelling asymmetric pulses within the framework of finite-rate-of-innovation (FRI) signals. We use the fractional Hilbert transform to model asymmetry in the pulse shape. The annihilating filter is employed to estimate the locations of the pulses. The asymmetry of the pulses manifests as a complex phase factor in the Fourierdomain expression of the signal. We model a single QRS complex of an electrocardiogram (ECG) signal as a sum of a symmetric Gaussian and its Hilbert transform, which is antisymmetric. Since the Hilbert transform of a Gaussian pulse is not compactly supported, we truncate it using a Hamming window. We apply the proposed technique to three ECG datasets: ECG of healthy person having normal cardiac conditions, person with left ventricular hypertrophy, and person suffering from right ventricular hypertrophy. A comparison of the estimated amplitude and asymmetry parameters for the three datasets is shown, and a preliminary diagnostic tool for characterization of ventricular hypertrophy is proposed.