Thesis (Ph. D.)--Catholic University of America. / Vita.

Thesis (Ph. D.)--Catholic University of America. / Vita.

Thesis (Ph.D.)--Catholic Univ. of America. / Vita.

Electrocardiogram (ECG) time-domain signals contain important information about the heart. Several techniques have been proposed for creating a two-dimensional visualization of an ECG, called a Cardioid, that can be used to detect heart abnormalities with computer algorithms. The derivative method is the prevailing technique, which is popular for its low complexity, but it can introduce distortion into the Cardioid plot without additional signal processing. The Hilbert transform is an alternative method which has unity gain and phase shifts the ECG signal by 90 degrees to create the Cardioid plot. However, the Hilbert transform is seldom used and has historically been implemented with a computationally expensive process. In this thesis we show a low-complexity method for implementing the Hilbert transform as a finite impulse response (FIR) filter. We compare the fundamental differences between Cardioid plots generated with the derivative and Hilbert transform methods and demonstrate the feature-preserving nature of the Hilbert transform method. Finally, we analyze the RMS values of the transformed signals to show how the Hilbert transform method can create near 1:1 aspect ratio Cardioid plots with very little distortion for any patient data.

The thesis is focused on the properties of the selected plane curves of order higher than two and one transcendent curve. To each curve an overview of its properties which are then derived and described in detail is given. All curves are enriched with their images that are created in mathematical software GeoGebra. In addition, to these images the text links directly to GeoGebra are added, where some interesting features are described and demonstrated.