The joint optimization method of the graph filter design: the vertex sampling and the integration method

This article proposes and designs a new type of joint graph filter, which is based on the design of two commonly used general filters, that is, the vertex sampling method and the sum-of-squares integration method. A joint optimization of the graph filter is proposed to organically combine the two methods, and redesign the graph filter coefficients. This method can reflect the advantages of both design methods, thereby obtaining a more stable and smoother graph filter. The obtained filter can effectively control the noise amplitude and the ripple amplitude of the cutoff band of the graph filter in the initial phase of the response. This article demonstrates through theoretical analysis and numerical experiments that this method outperforms the basic method in designing the desired graph filter in terms of frequency response.