Adaptive level-crossing sampling and reconstruction

We propose an adaptive level crossing approach for the sampling and reconstruction of signals for applications where clock-free and low-power data gathering are required. Due to the lack of a priori information on the signal statistics, uniform levels are typically chosen in level-crossing (LC) sampling. Our approach uses as reference levels the local means obtained from an asynchronous sigma delta modulator (ASDM). This signal-dependent sampling constitutes non-uniform sampling with local means and their times of occurrence. The local means can be seen as optimal signal estimators in a mean-square sense. The reconstruction of the original signal is approached using Prolate Spheroidal Wave functions which performs well when the signal is time-limited and essentially band-limited. The optimality of the levels can be illustrated when comparing our procedure with uniform LC sampling and reconstruction. The proposed procedure is especially suited for applications where the signal occurs in bursts, and data gathering is done under clock-free, low-power and low-transmission conditions.