Application of Daubechies Wavelet Transform in the Estimation of Standard Deviation of White Noise

Aiming at an additive white noise, a method to estimate the standard deviation of white noise is presented in the paper. The sampled data are first transformed to the wavelet domain by wavelet transform with the different scale levels and the different lengths of the compactly supported wavelets, and then the wavelet coefficients at each level are employed to estimate the standard deviation of the noise directly, which avoids the sequencing operation of the wavelet coefficients carried out in the method to estimate the standard deviation by a median value. Examples prove that the method presented in the paper has the advantage over the method to estimate the standard deviation by a median value. In addition, it can be seen from the results calculated at the different scale levels and different lengths of the compactly supported wavelets that the scale level has a bigger influence on the estimation of the standard deviation of the noise, and that the length of the compactly supported wavelets has only a smaller influence on the estimation of the standard deviation of the noise.