Wavelet Filtering by Using Nonthreshold Method and Example of Model Doppler Function

The paper is devoted to the comparative analysis of the efficiency of two methods of discrete wavelet filtering. The first method consists in zeroing of the detailing coefficients up to a specific decomposition level, the determination of which was not investigated in the available publications, while the second method is often applied in practice and involves the use of common constrained threshold of detailing coefficients for all the decomposition levels. For finding the level of wavelet decomposition ensuring the minimal filtering error in time domain, the root-mean-square error of model was employed. In this case, the cosine and correlation distances reflect the filter performance efficiency as was revealed on the basis of results of their comparison with Euclidean norms of vectors in frequency domain. The analysis of wavelet filtering efficiency implies the need to divide the plane of noise distribution laws into two areas: one with the laws close to the normal distribution and the second with all the other laws. For the first group of noises with distribution close to normal, the relationship of the filtering error as a function of the decomposition level features a pronounced extreme character (i.e., minimum) making it possible to design simple filters with minimal computational costs by using the minimum error criterion. The comparison of the proposed filtering method with the classical Butterworth filter resulted in obtaining the identical errors with other factors being equal.