Abstract
We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the input, before obtaining the timing information using a time encoding machine. Within this framework, we show that sampling by timing is equivalent to a non-uniform sampling problem, where the reconstruction of the input depends on the characteristics of the filter and on its non-uniform shifts. The classes of filters we focus on are exponential and polynomial splines, and we show that their fundamental properties are locally preserved in the context of non-uniform sampling. Leveraging these properties, we then derive sufficient conditions and propose novel algorithms for perfect reconstruction of classes of non-bandlimited signals such as: streams of Diracs, sequences of pulses and piecewise constant signals. Next, we extend these methods to operate with arbitrary filters, and also present simulation results on synthetic noisy data.
Highlights
Sampling plays a fundamental role in signal processing and communications, achieving the conversion of continuous time phenomena into discrete sequences [1]
Acquisition models inspired by this mechanism include zero-crossing detectors [13], delta-modulation schemes [14], as well as the time encoding machine (TEM) introduced in [15]
At the local pixel-level, this is equivalent to time encoding of piecewise constant signals, which is studied in this paper. Motivated by these real-world applications, the time encoding strategy we propose is based on filtering the input signal before extracting the timing information using a crossing or an integrate-and-fire TEM
Summary
Sampling plays a fundamental role in signal processing and communications, achieving the conversion of continuous time phenomena into discrete sequences [1]. We initially develop our reconstruction framework for the case of one Dirac, where we show how a linear combination of its non-uniform samples leads to a sequence of signal moments, which can be annihilated using Prony’s method [38], in order to retrieve the free parameters of the input We extend this method to reconstruct infinite streams and bursts of Diracs, sequences of pulses as well as piecewise constant signals, for which we can achieve local reconstruction given the compact support of the filter. Please note that the code to reproduce our simulations is available online [39]
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