时间序列处理中一阶分形模糊滤波器效果分析

Analysis of First-order Fractal Fuzzy Filter in Time Series Process

一阶分形模糊控制滤波器是一种自适应滤波器,根据噪声的分形特征量变化改变滤波器的控制参数,自动调整其滤波特性,可以应用于时间序列的处理中。分析了一阶分形模糊控制滤波器的频率-幅度特性,白噪声和有色噪声分形盒维数的变化;讨论了滤波器中时间序列的短时分形盒维数的定义及分形模糊控制函数形式及选用方式。针对一个低频信号混杂不同有色噪声的时间序列的滤波处理算例表明分形模糊控制滤波器能够提高信噪比,相对固定滤波器具有较小的均值误差;但是其过于简单的结构和对时间序列分形特征量应用的不准确影响其性能。提出改变分形模糊滤波器结构、利用噪声多重分形特征量并采用神经网络、查表法确定模拟控制函数等来改善分形滤波器性能的方法。

First-order fractal fuzzy control filter is a kind of adaptive filter, and it adjusts its performance by changing control parameter according to the change of fractal property of noisy signal, and can be used in time series processing. The frequency-magnitude response of the fractal filter and the change of fractal box dimension of white noise and color noise are analyzed. The definition of short-time fractal box dimension and the fuzzy control function of the filter are discussed. Simulation results of a low frequency signal mixed with noise processed by the filter show that the fuzzy control filter can enhance signal-to-noise ratio and has less mean-square error than that of fixed filter; Nevertheless, the oversimplified structure and the inaccurate application of the fractal character of time series degrade the performance of the filter. The improvement approaches as adoption of new architecture, multifractal character of noise, neural network and table-looking methods in choosing control function are presented at last.