The effect of redundancy on measurement

This correspondence demonstrates that increasing the number of measurements made on a system beyond the minimum (i.e., the number of degrees of freedo m in the system) can reduce the effect of measurement errors. The correspon dence shows, for three broad classes of measurement problems, that, as the measurement redundancy increases, the residual error falls to a small const ant value. Twice the number of degrees of freedom will allow performance ve ry close to the ultimate limits. The correspondence presents one example wi thin each class; however, a vast number of other measurement problems have a formulation identical to one of these three. The first example is the cal ibration of a resistive voltage divider consisting of a number of nominally equal resistors in series. The second is the determination of the complex response of a filter whose output can be observed only through a power dete ctor. The third is the calibration of a resistive current combiner or curre nt mode digital-to-analog converter (DAC). The basic ideas in the correspon dence are general and extensions to other measurement problems outside of t he three categories should be straightforward, although the details of the solution will be problem dependent.