Reconstruction methods for level-crossing sampling

Abstract

Level-crossing sampling refers to a sampling method that generates a sequence of timing samples when a signal crosses a specified set of levels. Conventional sampling techniques more typically rely on producing a sequence of amplitude samples at a specified set of timings. Level-crossing sampling has been considered as a promising alternative to time sampling when it is difficult to implement high-precision quantizers but where high timing resolution is possible. Although Logans theorem provides conditions in which signals are recoverable from samples obtained by zero-crossing, which is a level-crossing sampling method with one level, associated conditions for a multi-level framework have not yet been developed. This thesis studies a recently proposed level-crossing sampling method, which corresponds to amplitude sampling. This method establishes an amplitude-time relationship representation of the original signal, which is referred to as the amplitude-time function. The pre-designed levels determine when samples of the amplitude-time function are taken. This sampling procedure enables us to design two algorithms, the Bandlimited-Interpolation Approximation (BIA) algorithm and the Iterative Amplitude Sampling Reconstruction (IASR) algorithm, that can reconstruct the original signal from these timing samples with improved accuracy over existing multi-level-crossing sampling approaches. By relating amplitude sampling with nonuniform time sampling, we further compare these algorithms with one of the more efficient nonuniform time sampling methods, the Adaptive Weights Method (AWM). Simulations show that not only do these two algorithms attain high signal-to-error ratio (SER), but the IASR can generally reconstruct the original signal with fewer iterations than the AWM.