The Design of a New Non-linear Predictive Filter

The paper presents a new method to design a predictive filter which suits to analyze non-stationary data. The processed data are approximated by polynomial. The approximating function in the paper is cubic spline. The predictive filter is constructed with the true value and the observation value of each observation point. The designed filter can perform adaptive analysis to the observation data, and is able to implement multi-resolution analysis as wavelet transform. The paper discusses the derivation of the filter in detail and analyzes its amplitude-frequency characteristics, and then presents the decomposition and composition structure when using the filter to analyze data.