Digraph Filter Design Based on Directed Laplacian Matrix and Least Squares Method

In this paper, the digraph filter design based on directed Laplacian matrix (DLM) and least squares method is presented. First, the eigen-decomposition of DLM is used to define the digraph Fourier transform (DGFT). Then, the spectral properties of DGFT are studied and applied to specify the ideal spectral response of the digraph filter. Next, the coefficients of polynomial and rational digraph filters are determined by the least squares method which minimizes the integral absolute squared errors between ideal response and actual spectral response of filter. The matrix inversion can be used to compute the optimal solution. Finally, the proposed method is compared with conventional design methods to evaluate performance and the signal denoising application examples are demonstrated to show the effectiveness of the designed digraph filters.