混合力オス信号の独立成分分析と力オス解析

摘要

The key ingredient of signal analysis is to find a set of "natural basis functions- which are orthogonal to each other and which can be used as an orthogonal expansion basis. Our recent findings by simulations and experiments in a real physical environment that chaotic mixtures can blindly be separated into "natural chaotic sources" show that such chaotic sources can be used as orthogonal basis functions for spectrum analysis. Next, we show that such spectrum analysis based on the generalized Fourier expansion in terms of chaotic basis functions can be constructed by using Lebesgue spectrum analysis of ergodic theory. Furthermore, mixing property is proven by the existence of a complete orthonormal function of Lebesgue spectrum and finally a new orthogonal code based on the primitive root of a prime p called primitive root code is introduced for our chaotic spectrum analysis.