A Fast Amplitude Approximation For Quadrature Pairs

Abstract

This paper gives an algorithm from which an approximation to the amplitude of a quadrature pair can be obtained simply and without requiring more bits than are needed to represent the largest allowable amplitude, A. If A cos θ and A sin θ are a quadrature pair, the amplitude is $A=(A^{2}cos^{2}theta + A^{2}sin^{2}theta)^{1over 2}.$ If AX is the larger magnitude of the pair and AY the smaller, an approximation to A is $A^{prime} = AX + {1over 2}AY.$ Computations using this algorithm with random values of θ showed that when the true amplitude was A, the mean obtained was 1.087A, with standard deviation 0.031A. When A consists of a signal appreciably contaminated with noise so that several estimates are required before the signal can be detected reliably, no significant degradation («0.1 dB S/N) in detectability was found using the algorithm described above.