Alexander fractional differential window filter for ECG denoising.

The electrocardiogram (ECG) non-invasively monitors the electrical activities of the heart. During the process of recording and transmission, ECG signals are often corrupted by various types of noises. Minimizations of these noises facilitate accurate detection of various anomalies. In the present paper, Alexander fractional differential window (AFDW) filter is proposed for ECG signal denoising. The designed filter is based on the concept of generalized Alexander polynomial and the R-L differential equation of fractional calculus. This concept is utilized to formulate a window that acts as a forward filter. Thereafter, the backward filter is constructed by reversing the coefficients of the forward filter. The proposed AFDW filter is then obtained by averaging of the forward and backward filter coefficients. The performance of the designed AFDW filter is validated by adding the various type of noise to the original ECG signal obtained from MIT-BIH arrhythmia database. The two non-diagnostic measure, i.e., SNR, MSE, and one diagnostic measure, i.e., wavelet energy based diagnostic distortion (WEDD) have been employed for the quantitative evaluation of the designed filter. Extensive experimentations on all the 48-records of MIT-BIH arrhythmia database resulted in average SNR of 22.014 ± 3.806365, 14.703 ± 3.790275, 13.3183 ± 3.748230; average MSE of 0.001458 ± 0.00028, 0.0078 ± 0.000319, 0.01061 ± 0.000472; and average WEDD value of 0.020169 ± 0.01306, 0.1207 ± 0.061272, 0.1432 ± 0.073588, for ECG signal contaminated by the power line, random, and the white Gaussian noise respectively. A new metric named as morphological power preservation measure (MPPM) is also proposed that account for the power preservance (as indicated by PSD plots) and the QRS morphology. The proposed AFDW filter retained much of the original (clean) signal power without any significant morphological distortion as validated by MPPM measure that were 0.0126, 0.08493, and 0.10336 for the ECG signal corrupted by the different type of noises. The versatility of the proposed AFDW filter is also validated by its application on the ECG signal from MIT-BIH database corrupted by the combination of the noises as well as on the real noisy ECG signals are taken from MIT-BIH ID database. Furthermore, the comparative study has also been done between the proposed AFDW filter and existing state of the art denoising algorithms. The results clearly prove the supremacy of our proposed AFDW filter.