Opportunistic Sampling by Level-Crossing

This dissertation addresses an alternative sampling method called level-crossing (LC). In recent years LC has emerged as an alternative to the traditional Nyquist-Shannon based sampling. While the conventional approach is an ideal enabler of reliable and perfect signal reconstruction, it is not always economical and efficient. LC is a threshold-based sampling that is particularly suitable for processing bursty signals, which exist in a diverse range of settings. The motivations for this work are twofold: one is to address signal reconstruction outside of the conventional paradigm, and the other is to address compression in data processing. This work makes the following contributions: 1. consistent reconstruction algorithm via LC for a general class of signals, 2. perfect reconstruction algorithm via LC for signals of finite rate of innovation, 3. a universal sequential algorithm for the placement of reference levels that is competitive with the best static scheme known a priori, and 4. a numerical index that measures signal sparseness which is used to analytically show the relationship between rate of transmission and signal characteristics. The framework established in this work aims to capture the full potential of LC. Insights gained from the analytical work will contribute to the establishment of new data acquisition protocols and provide references for hardware implementations of LC ADCs. i