Applied Research Of Wavelet Analysis In Fractal Signals

Fractal signal widely exists in nature. As an emerging theory, it had attracted world-wide concern since its birth. An important character of the fractal signal is local self-similarity shown in the time domain. This suggests people that: wavelet transform, with its ability of scale analysis, may be a proper tool for analyzing fractal signal.This paper firstly discussed its main topics and relevant background, then, related theory of fractal signal and wavelet theory are described in detail. The following part mainly studied the application of wavelet analysis in fractal signal used in denoise and modulation schemes, and achieved better performance. The main contents are listed as following:1. To solve the problem of simulating fractal signal, we proposed using wavelet function to obtain fractal signal, and this method was applied in MATLAB.2. To extract the useful signal from fractal noise, we proposed a new denoising algorithm based on wavelet transform. Numerical simulation and experimental results show that the method can adaptively and effectively extract the useful signal from the fractal noise,3. We studied relevant theories of wavelet fractal modulation and its digital implementation. In fractal modulation, analog implementations has been studied in detail, but this method only applies for analog communication systems, for the digital age, digital communications become very popular, so for how to implement the digital fractal modulation is a key study of the recent years. This thesis based on the basic theoretical knowledge of wavelet fractal modulation, studied how to establish a digital wavelet fractal modulation system and demodulation system and numerical simulation and experiment was implemented to demonstrate its feasibility and efficient.