Frequency Selective Analog to Digital Converter Design: Optimality, Fundamental Limitations, and Performance Bounds

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Event Speaker: 

Mitra Osqui

Event Location: 

32-D677

Event Date/Time: 

Tuesday, December 4, 2012 - 4:00pm

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.

Adviser: Alexandre Megretski
Committee: Munther Dahleh and Pablo Parrilo