Both fundamental theory and design algorithms are developed for systems which convert analog data into digital representation. The examples of principal interest are oversampled analog-to-digital converters (ADC) and vector quantization systems. The latter emphasizes low-rate communications and data storage systems where the PI has made significant contributions in the past. The former emphasizes recently developed architectures for high rate ADC by using scalar feedback binary quantizers at a sampling rate much higher than the Nyquist rate. An additional research topic is the interplay between these systems, e. g. the use of an oversampled ADC front end to a data compression system using vector quantization. The main application area for this work is speech transmission and recognition. Signals exist mainly in analog form, thus prior to digital processing they must be sampled and converted to finite-length computer words by a process called quantization. This task is performed by the so-called analog-to-digital converter (ADC). The PI brings new mathematical methods to bear on the analysis of oversampled ADC's, a particularly attractive class of quantizers from the implementation point of view.
