Numerical Implementation of the Hilbert Transform

by Wang, Xiangling

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 ease of software and hardware implementations, an efficient approach (the Remez approach) for use in calculating the Hilbert transform to build a Holter Monitoring System is proposed.

Using the Parks-McClellan algorithm, the Remez approach was present, and a digital filter was developed to filter the data sequence.

Accurate determination of the QRS complex, in particular, accurate detection of the wave peak, is important in ECG analysis and is another task in this thesis. A program was developed to detect the wave peak in an ECG wave.

The whole algorithm is implemented using Alteras Nios SOPC (system on a program chip) Builder system development tool. The performance of the algorithm was tested using the standard ECG waveform records from the MIT-BIH Arrhythmia database. The results will be used in pattern recognition to judge whether the ECG wave is normal or abnormal.