Mathematics of Analog-to-Digital Conversion
Article first published online: 27 SEP 2012
Copyright © 2011 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Special Issue: Second Special Issue Commemorating the 75th Anniversary of the Courant Institute
Volume 65, Issue 12, pages 1671–1696, December 2012
How to Cite
Güntürk, C. S. (2012), Mathematics of Analog-to-Digital Conversion. Comm. Pure Appl. Math., 65: 1671–1696. doi: 10.1002/cpa.21425
- Issue published online: 27 SEP 2012
- Article first published online: 27 SEP 2012
- Manuscript Received: OCT 2011
As the performance of digital circuits and the capacity of digital communication channels have advanced steadily over the past decades, digital signals have replaced analog signals in nearly every technological application domain, offering robustness, ever increasing quality, and speed. At the same time, many signals that we perceive audiovisually (sound and video), or measure via instrumentation (e.g., geophysical signals and medical images), are analog in their nature. Consequently, not only are the analog-to-digital (A/D) and digital-to-analog (D/A) conversion processes as crucial as ever, but also the performance of these processes must improve to meet the increasing demands at the digital processing end. Both A/D and D/A conversion is necessarily carried out via analog devices bound by physical limitations such as imprecisions and noise, which present continual technological as well as theoretical challenges to achieving this objective. This article aims to introduce some of the modern mathematical ideas, developments, and challenges in this context from the author's perspective. © 2012 Wiley Periodicals, Inc.