Definition of a Graph Cepstrum for Homomorphic Processing of Graph Signals

In recent years, with the increase of complex and irregular data in our everyday lives, graph signal processing has gained popularity especially among the signal processing researchers. In this manuscript, we define graph cepstrum as a new tool which could be applied for homomorphic processing of graph signals. Our motivation in defining graph cepstrum was the successful application of conventional cepstrum in speech processing for determining pitch period. In this manuscript, as an example, we also present an application of graph cepstrum using a synthetic graph signal. It is our belief that, in future applications, graph cepstrum could also be used advantageously in processing of certain real-world graph signals.