Design of a Filter Based on Polynomial Interpolation and Local Fit

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. An interpolation filter design method based on local polynomial fit algorithm was presented in this paper. By comparing the differences and relations of the two filters, it is discovered that Deslauriers-Dubuc interpolation filter may be regarded as one special filter of polynomial interpolation and local fit filter. The simulation result of signal denoising show that the filter based on polynomial interpolation and local fit can make better use of the data, and is more robust for denoising.