Minimax Design of Computationally-Efficient FIR Graph Filters Using Semidefinite Programming

We propose a minimax design method for finite impulse response (FIR) graph filters in this brief. We first convert the graph filter design problem into a numerically stable equivalent problem using a shifted monomial basis. Then, we convert the minimax graph filter design problem into a semidefinite programming problem. Furthermore, we propose a computationally-efficient structure to implement the FIR graph filters designed using the proposed method. Design examples confirm that the proposed method can be used to design FIR graph filters having reasonably high orders, and the proposed implementation structure substantially saves additions required to process a graph signal compared to graph filters designed using a previously proposed Chebyshev polynomial approximation method.