A synthetic sensitivity — roundoff design

Abstract

In classical analysis, the two Finite Word Length effects due, respectively, to coefficient truncation and to arithmetic roundoff are investigated separately. We have seen in Chapter 3 that, when the L₁/L₂ measure is adopted as a transfer function sensitivity measure, the realizations that minimize this L₁/L₂ measure are not the same as those that minimize the roundoff noise gain, G. However, under an l₂ constraint on the states, the realizations that minimize G also minimize the upper bound of the L₁/L₂ measure. It is not clear what the connection might be — if any — between realizations that minimize the roundoff noise gain G (under l₂ constraints) and those that minimize the more realistic L₂ sensitivity measure.