@article{(Open Science Index):https://publications.waset.org/pdf/12268, title = {Discrete Polynomial Moments and Savitzky-Golay Smoothing}, author = {Paul O'Leary and Matthew Harker}, country = {}, institution = {}, abstract = {This paper presents unified theory for local (Savitzky- Golay) and global polynomial smoothing. The algebraic framework can represent any polynomial approximation and is seamless from low degree local, to high degree global approximations. The representation of the smoothing operator as a projection onto orthonormal basis functions enables the computation of: the covariance matrix for noise propagation through the filter; the noise gain and; the frequency response of the polynomial filters. A virtually perfect Gram polynomial basis is synthesized, whereby polynomials of degree d = 1000 can be synthesized without significant errors. The perfect basis ensures that the filters are strictly polynomial preserving. Given n points and a support length ls = 2m + 1 then the smoothing operator is strictly linear phase for the points xi, i = m+1. . . n-m. The method is demonstrated on geometric surfaces data lying on an invariant 2D lattice.}, journal = {International Journal of Computer and Information Engineering}, volume = {4}, number = {12}, year = {2010}, pages = {1993 - 1997}, ee = {https://publications.waset.org/pdf/12268}, url = {https://publications.waset.org/vol/48}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 48, 2010}, }