Polynomial Graph Filter Design Using Legendre Polynomials

Polynomial graph filter (PGF) is an important tool for processing the irregular data captured from various complex networks, so the design of PGF is studied in this paper. First, Legendre polynomials are briefly reviewed and the basics of graph signal processing (GSP) are described. Second, the PGF design using Legendre polynomials is presented. The closed-form solution of filter coefficients is derived for lowpass, bandpass and highpass filters. Third, an efficient implementation structure of PGF based on recurrence relation of Legendre polynomials is investigated. Finally, the signal denoising application of sensor network data is demonstrated to show that the PGF method has better performance than the conventional smoothness-based method in term of the improvement of signal to noise ratio.