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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. [ABSTRACT FROM AUTHOR]

White Gaussian noise (WGN) commonly exists in acquisition and transmission of heart sound (HS) signals. The energy distributions of WGN and HS in wavelet decomposition levels (WDLs) are explored. The statistical analysis indicates that for WGN, energy proportions of detail portions of WDLs and energy proportion of the 2nd WDL are fixed. This finding is verified by using Monte Carlo test. Moreover, for a HS signal recorded under sampling frequency of 4 kHz, energies of the 1st and 2nd WDL are almost the same, which are validated by theoretical analysis and practical observation on three HS benchmark datasets. Based on these findings, equations estimating WGN energy and signal to noise ratio (SNR) for a noisy HS signal are created. In addition, a novel energy distribution-based wavelet multi-threshold de-noising approach (ED-WMTD) is proposed to reduce WGN. In which, firstly based on the energy distribution in WDLs and estimated energy of WGN, WGN energy in detail portion of each WDL is figured out. Then, soft-threshold method is adopted. The best threshold in a WDL is defined as the one by which the energy loss of noisy HS signal in this WDL is most similar to the energy of WGN in detail portion of this WDL. The accuracy of such a WGN energy estimation method is evaluated by average error of SNR estimation. ED-WMTD is assessed using mean square error and compared with four generally used WMTD methods. Experimental results show that this novel HS de-noising approach not only filters out HS noise effectively but also well retains its pathological information. [ABSTRACT FROM AUTHOR]