White noise energy and SNR estimation based on haar wavelet decomposition for heart sound and electrocardiogram signals

Abstract

The law of energy distribution of White Noise (WN) in Haar wavelet decomposition levels (WDLs) of heart sound (HS) and electrocardiogram (ECG) signals is analyzed statistically. The analytical results indicate that for WN signals, energy proportion of the 2nd WDL to the 1st WDL is fixed. For HS and ECG signals, when sampling frequency is 4 kHz for HS or 400 Hz for ECG, energies of the 1st WDL and 2nd WDL are almost the same. Based on the wavelet energy distribution laws of HS, ECG and WN, equations are created to estimate WN energy and signal to noise ratio (SNR). Numerical results show that the new WN energy and SNR estimation method has the normalized mean square error of less than 0.1 in all cases considered. © 2014 Springer-Verlag Berlin Heidelberg.