Abstract: The filter(convolution) commonly used in signal processing and image editing.In the paper, the sub-spectrum filter is represented by polynomial linear harmonic, and the principal components analysis was used to extracting influential sub-spectrum filter.This method expand the spectrum to continuously infinite number of dimensions by applying the approach which is knowing as spectral theory.The experiments showed that the proposed algorithm can extract multiple representative sub-spectrum filter, discrete the eigenimage (a 2D image which is affected by the sub-spectrum). At the same time, this paper uses the four evaluation criteria in order to verify that Laplace filter kernel polynomial is same as ordinary Laplace filter kernel.The last part of the experiment also proofs that the algorithm can be used to recover filter kernel.