Consensus-Based Signal Transform: A Novel Method to Represent Discrete-Time Signals as Graphs
Manolis Mylonas, Leontios Hadjileontiadis, Georgios Apostolidis · 2024
Signal transform and new time series representations are crucial for advancing signal processing techniques. This letter introduces the consensus-based signal transform (CBST), a method to represent a time series as a weighted undirected graph, a linear combination of base graphs. Within CBST, each graph's topology is determined by maximizing the collective frequency response, measured by the rate of change in the state variables of all nodes in response to an input signal. The state variables are updated using a linear distributed consensus protocol, which filters different input time series frequency components. The resulting graph topology resonates with specific frequencies. Base graphs are produced for each dominant frequency, and their weighted sum forms the graph representation of the input time series. Mathematical analysis and examples demonstrate the CBST's validity and potential applications, offering a new perspective on signal processing.