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Reconstructing Classes of Non-Bandlimited Signals From Time Encoded Information
IEEE Transactions on Signal Processing ( IF 5.230 ) Pub Date : 2019-12-20 , DOI: 10.1109/tsp.2019.2961301
Roxana Alexandru; Pier Luigi Dragotti

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.
更新日期:2020-02-07

 

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