effective number of bits
A.P. Kazantsev, A.M. Abramov
Various methods of physicochemical biology depend on the high-resolution recording of weak low-frequency signals (pH-metering, ionometry, micro-fluorimetry, micro-spectrometry, micro-calorimetry, etc). The same is valid also in medicine, for example, in cardiotocography. The term High Resolution implies either the high Signal-to-Noise ratio or the sensitivity in detecting the small changes of signal level. In spite of the two characteristics both can be defined in several manners the minimal noise level is always required. This is all the ways connected to the number of bits for the numerical representation of the measured value. However either the last significant bit or the most steady one is considered to be the last bit in the numeric. As soon as the instrument developer starts asking what is the accuracy requirement, he/she gets a counter question about the adequate characteristics of accuracy. Until recently such the characteristics considered to be statistical estimates of error, and now already (or also) it is necessary to use the uncertainty of measure-ments parameters.
The results of this work are followed:
proven definition of the acceptable standard uncertainty for the uniform analog-to-digital converter is given;
the analytical expression for the effective number of bits as information throughput capacity is suggested;
it is shown that the IEEE 1057-2007 standard expression for the effective bits overstates the accuracy estimate by 20 %;
the cost effective method for the development of low-bandwidth high-resolution recorders and the dependant sys