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.
No takes yet. Share an insight, caveat, or question.
Ekambaram et al. (2013) studied this question.