基于样条插值的非线性滤波器的分析与设计

Analysis and Design of Non-linear filters Based on Cubic Spline Function

在理论分析和实际应用中,信号分析具有重要的理论意义和实际应用价值。非平稳信号的分析及处理一直是学术和工程界关注的热点问题之一。由于传统数据分析方法受线性或者平稳性假设的限制,无法有效地应用于图像处理、语音处理及雷达信号处理等实际应用中。本文通过对非线性、非平稳数据的建模,研究了适合非平稳数据分析的经验数据分解算法。建立了可行的经验数据分解滤波器的设计准则,并利用三次样条插值预测滤波器的参数。使用超光谱图像数据进行测试分析,在一次经验数据分解后,分析了高频子带数值在规定范围内的概率分布及相应的熵值。实验结果表明:经验数据分解算法产生的高频系数在0附近更集中,这对图像压缩有利,从而证明经验数据分解是一种对非平稳数据有效的分析方法。

Signal analysis has important theoretical and practical application.Non-stationary signal analysis and processing is one of the hot topics in the scientific and engineering research area.Because of the limit of linearity and stationarity assumption,the traditional methods can not be effectively used in image processing,speech processing and radar signal processing.A model suiting for nonlinear and non-stationary is established.The empirical data decomposition algorithm is discussed.A suitable design criteria is established. The use of cubic spline functions to predict the parameters of the predictive filter is discussed.Making a test on spectrum image data with empirical data decomposition.The system is simulated in Mat lab.The probability distribution of the samples in high-frequency subbands whose values are within the specified range and the corresponding entropy are analyzed through simulation.The results show that the high-frequency coefficients produed by empirical data decomposition algorithm is more concentrated than those of 5/3 wavelet and 9/7 wavelet,which are useful to image compression,and also proved empirical data decomposition is an effective analysis method for non-stationary image data.