Harmonic Retrieval From Chaotic Background

A wide variety of natural phenomena exhibit complicated, unpredictable and seemingly stochastic behavior. Chaotic dynamics appears to provide a relatively simple and possibly more satisfactory explanation to a lot of complicated phenomena among them. Chaos theory shows that simple deterministic systems with only a few variables can generate seemingly stochastic behavior. The purpose of chaotic theory is discovering possible simple rules which hide in the seemingly random phenomena and obtaining common rules which a kind of complex phenomena keep to. Chaos is an outer complex behavior of nonlinear definite system, produced by the system's internal stochastic property, a non-stochastic movement while looks like stochastic. One of the basic characteristics is that the system is highly sensitive to original condition, that is to say, the little difference of original condition assumes exponential increase until it is unacceptable. Chaotic signal differs from traditional periodic signal and pseudo-periodic signal, it also differs from purely stochastic signal. Chaos is essentially deterministic, but the long-playing trend cannot be forecasted. The deterministic, pseudo-stochastic and short-time divinable characteristics of chaos make it have application value in some applying field, such as chaotic secure communications, electron counterwork. Chaotic signal processing is a fire-new branch of non-linear signal processing. It has abundant research tasks in natural and engineering field, such as ocean, geology, biology and chemistry et al. Nowadays, Chaotic signal processing becomes a pop science research field. As an important branch of chaotic signal processing, signal extraction from chaotic background has important theory and application value. For example, target signal extracted from sea clutter(which has been proved to be chaotic), fetal electrocardiogram extracted from matrix in biomedicine, weak signal extracted from visual evoked potential and resisting chaotic interference all belong to signal extraction from chaotic background. On the other hand, signal extraction blindly from chaotic background is the most important and effective means to attack chaotic secure communication. Doing research on signal separation blindly supply use for reference to chaotic secure communication. The creativity task of this paper focuses on three aspects: 1. The research of chaotic signal processing technology for extracting signal from chaos is still in its early development. In this paper, the methods in this field are summarized, especially, minimizing phase space volume method, local projection of attractor method, Stark prediction method, the nonlinear inverse of linear filter method and neural network method are discussed. The point of view for each method is analyzed, and a new technology for chaotic signal processing is put forward. 2. Wavelet transform is made to chaotic signal whose mathematic model is differential equation group, harmonic signal and white noise. According to the different characteristics of these signals in approximate part and detail part, an algorithm based on wavelet multiscale decomposition to extract harmonic from chaos is put forward. Then, taking example for Lorenz signal as chaotic background, a series of simulations are made. Through analyzing the experiment result, effectiveness of this algorithm is validated. Otherwise, comparing with existing algorithms, dispensing with reconstructed phase space, the algorithms are simpler and directer, have faster count speed and better estimate precision. 3. Based on soft-threshold and wavelet multiscale decomposition, an algorithm based on wavelet soft-threshold filtering is put forward to extract harmonic from noisy chaos. There are observation noise and noise of algorithm in application. The well denoising characteristic of this algorithm make it better than the algorithm based on wavelet multiscale decomposition. 4. The application of wavelet packet transform to harmonic retrieval from chaos is analyzed. The analysis implies that wavelet packet transform is not superior to wavelet transform. The dissertation consists of six chapters.