Asynchronous sampling and reconstruction of sparse signals

Asynchronous signal processing is an appropriate low-power approach for the processing of bursty signals typical in biomedical applications and sensing networks. Different from the synchronous processing, based on the Shannon-Nyquist sampling theory, asynchronous processing is free of aliasing constrains and quantization error, while allowing continuous-time processing. In this paper we connect level-crossing sampling with time-encoding using asynchronous sigma delta modulators, to develop an asynchronous decomposition procedure similar to the Haar transform wavelet decomposition. Our procedure provides a way to reconstruct bounded signals, not necessarily band-limited, from related zero-crossings, and it is especially applicable to decompose sparse signals in time and to denoise them. Actual and synthetic signals are used to illustrate the advantages of the decomposer.