Discrete-Time Randomized Sampling

Techniques for developing low-complexity, robust Digital Signal Processing (DSP) algorithms with low-power consumption have become increasingly important. This thesis explores a framework, discrete-time randomized sampling, which allows the design of algorithms that meet some desired complexity, robustness or power constraints. Three distinct sampling schemes are presented based on randomized sampling of the input, of the filter impulse response, and iterative randomized sampling of the filter impulse response. Additive noise models are derived for each approach and error characteristics are analyzed for both white and colored sampling processes. It is shown that semi-white iterative randomized sampling leads to better error characteristics than white sampling through higher SNR as well as noise shaping. Discrete-time randomized sampling is then used as a filter approximation method and conditions are derived under which a randomized sampling approximation to the Wiener filter is guaranteed to lead a smaller mean-square estimation error than the best constrained LTI approximation. A low-power formulation for randomized sampling is also given and the tradeoff between power consumption and output quality is examined and quantified. Finally, this framework is used to model a class of random hardware failures and two algorithms are presented that guarantee a desired SNR level at the output under a given probability of hardware failure. Thesis Supervisor: Alan V. Oppenheim Title: Ford Professor of Electrical Engineering