Frequency selective analog to digital converter design : optimality, fundamental limitations, and performance bounds

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 131-137).In this thesis, the problem of analysis and design of Analog to Digital Converters (ADCs) is studied within an optimal feedback control framework. A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. The performance measure is defined as the worst-case average intensity of the filtered input-matching error, i.e., the frequency weighted difference between the input and output of the ADC. An exact analytic solution with conditions for optimality of a class of ADCs is presented in terms of the quantizer step size and range, resulting in a class of optimal ADCs that can be viewed as generalized Delta-Sigma Modulators (DSMs). An analytic expression for the performance of generalized DSMs is given. Furthermore, separation of quantization and control for this class of ADCs is proven under some technical conditions. When the technical conditions needed for establishing separation of quantization and control and subsequently optimality of the analytical solution to ADC design problem are not satisfied, suboptimal ADC designs are characterized in terms of solutions of a Bellman-type inequality. A computational framework is presented for designing suboptimal ADCs, providing certified upper and lower bounds on the performance.by Mitra M. Osqui.Ph.D

Conditions for optimality of scalar feedback quantization

This paper presents novel results on scalar feedback quantization (SFQ) with uniform quantizers. We focus on general SFQ configurations where reconstruction is via a linear combination of frame vectors. Using a deterministic approach, we derive two necessary and sufficient conditions for SFQ to be optimal, i.e., to produce, for every input, a quantized sequence that is a global minimizer of the 2-norm of the reconstruction error. The first optimality condition is related to the design of the feedback quantizer, and can always be achieved. The second condition depends only on the reconstruction vectors, and is given explicitly in terms of the Gram matrix of the reconstruction frame. As a by-product, we also show that the the first condition alone characterizes scalar feedback quantizers that yield the smallest MSE, when one models quantization noise as uncorrelated, identically distributed random variables