Fractional Compound Integral with Application to ECG Signal Denoising

Abstract

Based on the commonly used Liouville and Weyl fractional integral definitions, we present Liouville fractional linear phase delay filter and Weyl fractional linear phase lead filter. Thanks to the reverse phase characteristics of Weyl filter, an overall zero-phase effect can be achieved by cascading a Liouville filter with a Weyl filter (Liouville---Weyl fractional compound integral), and cascading a Weyl filter with a Liouville filter (Weyl---Liouville fractional compound integral), respectively. Due to the inherent characteristics of fractional order and zero phase, our methods not only effectively suppress the phase distortion in the filtering process, but also better enhance the compromise capability between signal denoising and signal information retention than the conventional filtering methods do. The proposed methods are evaluated on Electrocardiogram (ECG) signals, by respectively adding disturbance and random noises to ECG records from the MIT-BIH Database, and studying SNR and MSE of the filter outputs. Compared with conventional fractional integral denoising methods, the results of the study demonstrate superior performances on visual sense and quantitative comparisons.