Graph QMF with flatness constraints

Graph signal processing is an emerging area that has a wide variety of applications, e.g. energy networks, transportation networks and neuronal networks. Narang and Ortega (2012) proposed the critically sampled two-channel filter bank for signals on undirected graphs using spectral graph theory. The design of graph QMF (Quadrature-Mirror-Filters) by Narang and Ortega (2012) is based on the Chebyshev polynomial approximation of the ideal Meyer function. The reconstruction error using this method can be quite large especially for low degree filters and the high-pass filters suffer from DC leakage. A simple method that is analytically based is presented here for the design of the graph QMF without DC leakage and with low reconstruction error. The filters have flat spectral response at the DC and aliasing frequencies.