The correction of observational data for instrumental band width

Abstract

ABSTRACTThe readings Φ(x) of an instrument with the apparatus functiong(x) are related to the true valuesf(x)of the observed function by the equationA three-point interpolation operator can be chosen to simulate the spreading action of a class of functionsg(x). Under certain conditions the interpolation operator has an exact inverse which, when applied to Φ(x), gives a function which is a better approximation tof(x). The accuracy obtained is discussed, and the effect of the method on the standard errors in the measurement is found.