ВІДТВОРЕННЯ СИГНАЛІВ ТА ЗОБРАЖЕНЬ ЗА БІСПЕКТРОМ У ПРИСУТНОСТІ ШУМІВ

Abstract

In a number of practical applications of digital signal processing, the process under study may include correlated spectral components or phase coupling. Extracting the phase relationships provides very important and useful information for the correct understanding, analysis, and description of the properties of physical phenomena generating these processes. However, such information is irretrievably lost when using classical methods of signal processing using energy statistics, i.e. second-order statistics. Obtaining estimates of signal parameters and analyzing them using third-order correlation functions and bispectrum makes it possible to learn much more about signal properties than when using conventional correlation functions. Estimating the bispectral density (third order spectral density), in contrast to estimating the energy spectrum, makes it possible not only to describe the characteristics of the observed process correctly, but also to preserve and, if necessary, extract the phase characteristics of the component, which includes the observed process. Therefore, in a number of applied tasks of telecommunications, as well as tasks of image processing and other bisection analysis, often serves as an effective tool of signal processing. The aim of the article is to study the feasibility of using a recursive algorithm when restoring a waveform and image by bispectrum in the noise environment. The following types of signals were selected for the study: rectangular, triangular, Gaussian impulses and signal-triplet. They were distorted with additive white Gaussian noise Test image was distorted by additive white Gaussian, pulsed, Poisson and multiplicative noises. Analysis of the signal recovery results indicates that as the noise power increases, the quality of the recovery decreases. The effect of random signal shift does not affect the shape of the recovered signal. Analysis of the image recovery results indicates image recovery, but this algorithm introduces distortions in the form of an offset