Revision of the Sampling Theorem
Bujor Mircea · 2016
Almost every aspect of modern life benefits at some point from electronic devices. Most of them are digital, and the data they receive is digitally sampled from a sensor at some point. The Sampling Theorem stands at the core of every data acquisition system design. Recent research shows there are certain situations where information is lost, if a signal is sampled according to the Sampling Theorem. The Sampling Theorem is supposed to be true regardless of the acquisition time. Mathematically it isn't. The revision of the Sampling Theorem is about the neglected aspect of acquisition time. The acquisition time is a very limited resource in real life, and sampling can go terribly wrong if the problem is not properly addressed. In this work, the time dimension of the Sampling Theorem is covered, together with requirements for short acquisition time. A proof is provided for insufficiency of current Theorem. Another proof is provided for the revised Sampling Theorem. A discussion of what was done wrong until now and then an example from previous research is discussed. It is shown the new Sampling Theorem can help extract more information from analog to digital domain. Every digital electronic equipment used today can benefit from being fed more information.