  We propose a weighted least-square (WLS) method to design autoregressive
moving average (ARMA) graph filters. We first express the WLS design problem as
a numerically-stable optimization problem using Chebyshev polynomial bases. We
then formulate the optimization problem with a nonconvex objective function and
linear constraints for stability. We employ a relaxation technique and convert
the nonconvex optimization problem into an iterative second-order cone
programming problem. Experimental results confirm that ARMA graph filters
designed using the proposed WLS method have significantly improved frequency
responses compared to those designed using previously proposed WLS design
methods.
