Numerical Implementation of the Hilbert Transform

I agree that the Library, University of Saskatchewan, may make this thesis freely available for inspection. I further agree that permission for copying of this thesis for scholarly purpose may be granted to the professor or professors who supervised the thesis work recorded herein or, in their absence, by the Head of the Department or the Dean of the College in which the thesis work was done. It is understood that due recognition will be given to me and to the University of Saskatchewan in any use of the material in this thesis. Copying or publication or any other use of this thesis for financial gain without approval by the University of Saskatchewan and my written permission is prohibited. ii ACKNOWLEDGEMENTS I wish to express my gratitude to the following people who not only made this thesis possible but also an enjoyable experience: Dr. Ronald J. Bolton: my supervisor, for his valuable guidance, criticisms and consistent encouragement throughout the course of this research work. My husband, Zhanghai Wang: for his love and encouragement. My parents, my sister Xiangrong Wang and brother-in-law Xianggang Yu: for the support they provided to me. Xing: for making me feel welcome. They will always be special friends in my life. The Department of Electrical Engineering: for supplying the opportunity to study in Canada and the necessary facilities with which to work. iii ABSTRACT Many people have abnormal heartbeats from time to time. A Holter monitor is a device used to record the electrical impulses of the heart when people do ordinary activities. Holter monitoring systems that can record heart rate and rhythm when you feel chest pain or symptoms of an irregular heartbeat (called an arrhythmia) and automatically perform electrocardiogram (ECG) signal analysis are desirable. The use of the Hilbert transform (HT) in the area of electrocardiogram analysis is investigated. A property of the Hilbert transform, i.e., to form the analytic signal, was used in this thesis. Subsequently pattern recognition can be used to analyse the ECG data and lossless compression techniques can be used to reduce the ECG data for storage. The thesis discusses one part of the Holter Monitoring System, Input processing. Four different approaches, including the Time-Domain approach, the Frequency-Domain approach, the Boche approach and the Remez filter approach for calculating the Hilbert transform of an ECG wave are discussed in this thesis. By comparing them from the running time and the …