Estimating Sinusoidal Amplitude from Phase Noise and Jitter Corrupted Data Points

Estimating the amplitude of a sinusoidal signal from a set of data points using a least squares procedure is a common activity for an engineer. In real world applications those data points are inevitably perturbed by non-ideal phenomena of different origins. In the current publication the focus is on the effect of normally distributed phase noise or sampling jitter on the precision of the amplitude estimation. An analytical expression is derived that relates the amplitude estimation variance with the phase noise or jitter variance, the number of data points and sinusoidal amplitude. This result is useful for a scientist when trying to choose the proper number of points to acquire from a signal and when characterizing the precision of the estimates made by computing the confidence interval for a given confidence level.