Fast amplitude approximation yielding either exact mean or minimum deviation for quadrature pairs

Abstract

A computationally fast algorithm that yields an approximation to the amplitude A of a quadrature pair, AX and AY, is given by A'=AX + a ċ AY ≃A (=√AX²+ AY²) where a = 0.2673, AX is the larger magnitude of the pair, and AY the smaller. When the phase angle of pairs is uniformly distributed over the range (0, 2π), this algorithm yields the exact mean with the maximum deviation of 0.1039A. Thus this algorithm gives more accurate estimates than those obtained by Robertson's algorithm, which uses a of 0.5 and yields an error of 8.7 percent in the estimation of mean with the maximum deviation of 0.1180A.