On Time-Encoded Sampling for Multigenerator Shift Invariant Spaces

Time-encoded sampling represents an emerging paradigm for temporal discretization, garnering recent interest. In this paper, we address the challenge of time-encoded sampling for the perfect recovery of signals residing in shift-invariant spaces (SISs) defined by multiple generators. Specifically, we establish a sufficient condition for achieving perfect recovery of a signal from a multigenerator SIS when it is sampled using a single Time-Encoded Machine (TEM). This condition is exclusively characterized in terms of the provided set of multiple generators. Our findings extend the prior work of Gontier and Vetterli [ACHA, '13], which originally focused on single-generator SISs. We present illustrative results for both classic baseband signals and bandpass signals (both examples of SISs), highlighting the limitations of single-TEM-based time-encoding schemes.