Contribution of Jitter and Phase Noise to the Precision of Sinusoidal Amplitude Estimation Using Coherent Sampling

Estimating the amplitude of a sinewave from a set of data points is a common procedure in various applications. This is typically achieved using a least squares method that provides closed-form estimators. The sampling process itself is often affected by different non-ideal phenomena like additive noise, phase noise, or sampling jitter, for example. Here, the precision of the estimation of a sinewave amplitude when the samples are affected by phase noise or sampling jitter is studied in the case of coherent sampling. The mathematical expression derived is useful in obtaining the confidence intervals for the estimated sinusoidal amplitude. It is also valuable at the time of choosing the proper number of samples to acquire from a signal in order to reach a certain desired level of sinewave amplitude estimation precision. The analytical expression presented is validated using both numerically generated data and experimental data. Various non-ideal factors, such as a fixed, uncontrollable amount of jitter in the setup, additive noise, analog-to-digital converter non-linearity, and limited signal bandwidth, are observed and discussed. Additionally, this work presents an exhaustive overview of the technical aspects involved in the experimental validation, including the implementation of the Monte Carlo type procedure, instrument interface, programming language, and the general development of automated measurement systems, which may be useful to other engineers.