АНАЛИЗ И ПРОГНОЗИРОВАНИЕ ЭФФЕКТИВНОСТИ ФИЛЬТРАЦИИ ОДНОМЕРНЫХ СИГНАЛОВ НА ОСНОВЕ ДИСКРЕТНОГО КОСИНУСНОГО ПРЕОБРАЗОВАНИЯ

Abstract

The article deals with the analysis of the efficiency and expedience of applying filtering based on the discrete cosine transform (DCT) for one-dimensional signals distorted by white Gaussian noise with a known or a priori estimated variance. It is shown that efficiency varies in wide limits depending upon the input ratio of signal-to-noise and degree of processed signal complexity. It is offered a method for predicting filtering efficiency according to the traditional quantitative criteria as the ratio of mean square error to the variance of additive noise and improvement of the signal-to-noise ratio. Forecasting is performed based on dependences obtained by regression analysis. These dependencies can be described by simple functions of several types parameters of which are determined as the result of least mean square fitting. It is shown that for sufficiently accurate prediction, only one statistical parameter calculated in the DCT domain can be preliminarily evaluated (before filtering), and this parameter can be calculated in a relatively small number of non-overlapping or partially overlapping blocks of standard size (for example, 32 samples). It is analyzed the variations of efficiency criteria variations for a set of realizations; it is studied factors that influence prediction accuracy. It is demonstrated that it is possible to carry out the forecasting of filtering efficiency for several possible values of the DCT-filter parameter used for threshold setting and, then, to recommend the best value for practical use. An example of using such an adaptation procedure for the filter parameter setting for processing the ECG signal that has not been used in the determination of regression dependences is given. As a result of adaptation, the efficiency of filtering can be essentially increased – benefit can reach 0.5-1 dB. An advantage of the proposed procedures of adaptation and prediction is their universality – they can be applied for different types of signals and different ratios of signal-to-noise.