Closed-Form Designs of Frequency-Selective Graph Filters Using Polynomial Approximations

In this paper, closed-form designs of frequency-selective FIR graph filters using polynomial approximation methods are presented. First, the design problem of FIR graph filter is briefly described. Then, the Chebyshev polynomial approximation method is applied to design low-pass, high-pass and band-pass graph filters with closed-form solutions. Next, the Bernstein polynomial approximation method is used to design graph filters which have flat spectral responses. Finally, some design examples and graph signal de-noising application are demonstrated to show the effectiveness of graph filters.