Fractal Image Analysis of Wavelet Spectra of Linear Frequency Modulated Signals

The article deals with the fractal analysis of images of continuous wavelet spectra of radar signals with linear frequency modulation, taking into account the level of additive Gaussian noise and the frequency modulation coefficient. As a result of the analysis, the numerical value of the level of Gaussian noise additively added to the signal above which the identification of the terrain image or signal spectrum is impossible to be obtained. The Mexican Hat wavelet function, which provides the maximum range of fractal dimensionality variation with noise variation, is determined. Methods of threshold detection by proximity of series of scaled wavelet noise and signal scales are investigated. An example of the Shapiro-Wilk normality test has shown the inefficiency of using statistical methods to determine the noise threshold of the series of wavelet coefficients that form the images of spectra. Two methods of detecting the noise threshold versus global scalograms and autocoherence of the signal and noise transformed into wavelet coefficient series are considered. The autocoherence method is more efficient due to the availability of numerical values. For the identified thresholds of two frequency modulation signals, with and without additional amplitude modulation, spectrum images are obtained and maxima of fractal dimension at the noise threshold boundaries are determined. By numerical values of maxima it is suggested to identify spectra by noise threshold for neural networks, for example, for preparation of a set of recognizable images.