FRACTAL RADIOPHYSICS. Part 2. FRACTAL AND MULTIFRACTAL ANALYSIS METHODS OF SIGNALS AND PROCESSES

Abstract

Subject and Purpose. The subject of this paper is to review the principal methods of fractal and multifractal analysis of signals and processes, in combination with a detailed consideration of the algorithms that can provide for a successful practical implementation of the methods described. Methods and Methodology. The results presented concern modeling of both deterministic and stochastic fractal and multifractal signals and processes. The corresponding practical methods of analysis are considered, with discussion of their essential features, advantages and disadvantages, as well as of the problems of application that may exist. Results. Several approaches have been discussed as to categorizing the signals and processes within the notion of fractality. A few tens of models of deterministic and stochastic fractal or multifractal signals and processes have been analyzed in detail. Over twenty methods of monofractal analysis have been analyzed, with identifi cation of their features, advantages or disadvantages, and limits of applicability. The expediency of resorting to complex methods of monofractal analysis has also been discussed. Those methods are not based upon application of fractal analysis techniques alone but rather combine them with linear and nonlinear integral time-frequency transforms. The effectiveness of the ten most popular multifractal analysis techniques has been confirmed, with consideration of their special features, advantages and drawbacks. Conclusion. The mathematical foundations have been presented which underlie modern methods of analysis and modeling of fractal and multifractal signals and processes. The methods discussed may allow revealing a great amount of unique hidden information on the world around us.