Methods of discrete wavelet filtering of measuring signals: an algorithm for choosing a method

Abstract

When developing measuring instruments, taking into account the diversity of signals and factors affecting errors, the actual problem is the choice of the method of discrete wavelet filtering of measuring signals. The results of the development of an algorithm for choosing a discrete wavelet filtering method taking into account the nature of the measuring signal are presented. The three most common methods of discrete wavelet filtering are investigated, followed by a comparative analysis of twenty types of measurement signals. The following wavelet filtering methods are analyzed: with a common threshold for all levels of decomposition; without a threshold with a simple zeroing of the detail ratios until the minimum root-mean-square error of filtering the measurement signals is reached; with a universal threshold for the detail ratios at each decomposition level. We examined twenty types of measurement signals from the PyWavelets library, to which we added uncorrelated normally distributed noise with zero expectation and a given standard deviation. Method comparison criteria are defined for noisy signals before filtering and for filtered signals. The difference in signal-to-noise ratios, the difference in entropy errors, the rms filtering error, and the function of the measuring signal were used as criteria. For each filtering method, the comparison criteria are determined from the condition of the minimum root-mean-square error introduced by noise into the measuring signal of this type. When choosing a method, both energy and informational characteristics of signals were taken into account. The filtering parameters are determined by round-robin search to achieve the minimum root-meansquare filtering error. The proposed algorithm makes it possible to determine the most effective methods of discrete wavelet filtering, depending on the nature of the measuring signal. In this case, the developer simultaneously solves two problems: the choice of the filtration method and the determination of the filtration parameters.