TL;DR
This paper demonstrates that multi-channel time encoding can perfectly reconstruct bandlimited signals without knowing the shifts between channels, offering a more natural and robust sampling method inspired by biological neurons.
Contribution
It introduces a multi-channel time encoding framework that allows perfect signal reconstruction without shift knowledge, extending classical sampling theory to biologically inspired methods.
Findings
Multi-channel time encoding reconstructs signals with M times the bandwidth.
Reconstruction algorithm converges in noiseless conditions without shift information.
Multi-channel approach simplifies and improves robustness over classical sampling.
Abstract
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the devices have an unknown shift in their clocks. Alternatively, one can record the times at which a signal (or its integral) crosses given thresholds. This can model integrate-and-fire neurons, for example, and has been studied by Lazar and T\'oth under the name of ``Time Encoding Machines''. This sampling method is closer to what is found in nature. In this paper, we show that, when using time encoding machines, reconstruction from multiple channels has a more intuitive solution, and does not require the knowledge of the shifts between machines. We show that, if single-channel time encoding can sample and perfectly reconstruct a…
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