Information-theoretic approach to A/D conversion

We propose a new information theoretic approach to understanding analog-to-digital (A/D) conversion principles. An A/D converter is characterized as a communication system that transmits information from an analog source to the digital domain for processing, storage, transmission, and analysis. Accordingly, an A/D conversion system consists of an analog source of information, a means to sample and encode the analog signal for transmission through the comparator, and a means to decode the digital output from the comparator and provide a digital representation of the analog signal. The comparator acts as a channel since it 'injects' uncertainty in the form of quantization noise. We provide an upper bound (conversion capacity) on the amount of information that can be transmitted from the analog to digital domain for a specific A/D converter and we describe a necessary and sufficient condition that, if satisfied, allows an A/D converter to achieve capacity. The conversion capacity defines a fundamental upper limit on the performance of an A/D converter in terms of resolution-bandwidth product for a given technology. It is shown how the conversion capacity may be utilized to yield performance limitations in terms of mean square error and SNR. The capacity is, thus, a useful metric for the comparison of ADC designs and may also provide hints to improving existing and conceiving new A/D conversion methods.