Signal-to-noise ratio estimation based on Haar wavelet for cardiovascular bio-signals in web-based e-healthcare system

The law of energy distribution of white noise (WN) in Haar wavelet decomposition levels (WDLs) of cardiovascular bio-signals including Phonocardiogram (PCG), Electrocardiogram (ECG), and Sphygmogram (SPG) is analyzed statistically. The analytical results indicate that for WN signals, energy proportion of the 2nd WDL to the 1st WDL is 0.5 approximately, which is verified by Monte Carlo test. For PCG, ECG and SPG signals, when sampling frequency is 4 kHz for PCG, 400 Hz for ECG, and 160 Hz for SPG, energies of the 1st WDL and 2nd WDLs are almost the same; this is validated by theoretical analysis and practical observation on collected datasets. Based on the wavelet energy distribution laws of WN and cardiovascular bio-signals, equations are created to estimate energy of WN, energy of bio-signals, and SNR. Experimental results show that the proposed SNR estimation method for cardiovascular bio-signals mixed with WN has the normalized mean square error of less than 0.1 in all cases considered.