多项式插值与局部拟合的滤波器设计研究

Design of a filter based on polynomial interpolation and local regression

Deslauriers-Dubuc插值滤波器系统冗余较大,且对偶正则性较差,将Deslauriers-Dubuc插值滤波器推广到一般意义下的插值滤波器,对改善滤波器性能具有重要的意义。在研究Deslauriers-Dubuc插值滤波器的基础上,给出了基于多项式局部拟合的插值滤波器设计方法。通过比较二者之间的区别和联系,发现Deslauriers-Dubuc插值滤波器可以看作是多项式局部拟合插值滤波器的特例。信号去噪仿真试验表明,基于多项式局部拟合的插值滤波器能够充分利用数据的信息,对噪声具有较好的稳健性。

The drawbacks of commonly used Deslauriers-Dubuc interpolation filter are that the redundancy is large and dual-regularity property is not good. For improving the performance of the interpolation filter, the Deslauriers-Dubuc interpolation filter may be generalized to general interpolation filters. We present here an interpolation filter design method based on local and relations of the two filters, it is discovered polynomial regression that Deslauriers-Dubu algorithm. By comparing the differences c interpolation filter may be regarded as one special filter of polynomial interpolation and local regression filter. The signal de-noising experiment shows that the filter based on polynomial interpolation and local regression can make better use of the information, and is more robust for noise.