Reconstruction of a Gaussian Mean from Folded Data

Phasemeters are frequently constructed to alter phase data by folding it into a specified angular interval. As a result, the mean associated with folded measurements is usually shifted from that of the original distribution. When the underlying distribution is Gaussian, efficient unbiased estimators can be used to recover the true mean and variance (modulo 2¿) from folded data. The subsequent unwrapping of the folded measurements about this estimator will provide modulo 2¿ reconstruction of the original Gaussian distribution. Even if the original distribution is not Gaussian, determination of the Gaussian mean and variance, together with unwrapping, allows an analysis of how close to normal the original distribution is. The estimation procedure was used to reconstruct the phase distributions reported from several specific antenna elements. Gaussian behavior had been anticipated for the underlying distributions, but never verified. The results of this study provided support for the Gaussian assumption. In one surprising case, unwrapping of the phase distribution about its estimated mean allowed discovery of defects in the phasemeter hardware.