Sampling of Correlated Bandlimited Continuous Signals by Joint Time-vertex Graph Fourier Transform

TL;DR

This paper develops a sampling theory for multiple correlated bandlimited signals modeled as continuous time-vertex graph signals, establishing the minimum sampling rate for perfect recovery and proposing an efficient sampling scheme.

Contribution

It introduces a novel approach that exploits correlation in multi-signal sampling using graph Fourier transforms to minimize sampling rates for continuous signals.

Findings

Derived the minimum sampling rate for signal recovery.

Proposed a feasible sampling scheme based on correlation and graph transforms.

Validated the approach with theoretical proofs and simulations.

Abstract

When sampling multiple signals, the correlation between the signals can be exploited to reduce the overall number of samples. In this paper, we study the sampling theory of multiple correlated signals, using correlation to sample them at the lowest sampling rate. Based on the correlation between signal sources, we model multiple continuous-time signals as continuous time-vertex graph signals. The graph signals are projected onto orthogonal bases to remove spatial correlation and reduce dimensions by graph Fourier transform. When the bandwidths of the original signals and the reduced dimension signals are given, we prove the minimum sampling rate required for recovery of the original signals, and propose a feasible sampling scheme.