2019/05/08 by Roxana Alexandru, Alexandru, Roxana, Pier Luigi Dragotti +1 · 3 citations
Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Electrical engineering #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1905.03183
openalex publication_date 2019/05/08 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We investigate time encoding as an alternative method to classical sampling,\nand address the problem of reconstructing classes of non-bandlimited signals\nfrom time-based samples. We consider a sampling mechanism based on first\nfiltering the input, before obtaining the timing information using a time\nencoding machine. Within this framework, we show that sampling by timing is\nequivalent to a non-uniform sampling problem, where the reconstruction of the\ninput depends on the characteristics of the filter and on its non-uniform\nshifts. The classes of filters we focus on are exponential and polynomial\nsplines, and we show that their fundamental properties are locally preserved in\nthe context of non-uniform sampling. Leveraging these properties, we then\nderive sufficient conditions and propose novel algorithms for perfect\nreconstruction of classes of non-bandlimited signals such as: streams of\nDiracs, sequences of pulses and piecewise constant signals. Next, we extend\nthese methods to operate with arbitrary filters, and also present simulation\nresults on synthetic noisy data.\n