Circulant structures and graph signal processing

Linear shift-invariant processing of graph signals rests on circulant graphs and filters. The spatial features of circulant structures also permit shift-varying operations such as sampling. Their spectral features-as described by their Graph Fourier Transform profiles-enable novel multiscale signal processing systems and methods. To extend the reach of circulant structures, we present a method to decompose an arbitrary graph or filter into a combination of circulant structures. Our decomposition is analogous to resolving a linear time-varying system into a bank of linear time-invariant systems. As an application, we perform multiscale decomposition on temperature data spanning the continental United States.