###### Abstract  
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. devices like amplifiers, filters, and analog-to-digital converters (ADCs), among many other devices and systems. One also often uses sinewaves to measure different quantities like temperature [3] or distance [4]. In modern systems, often the signals from the real world are sampled, digitized, and input into computers for storage and processing. It is thus important to have signal processing algorithms that can estimate the various parameters of a sinewave like amplitude, initial phase, offset, and frequency. This estimation is generally made using a least squares procedure that minimizes the average of the squares of the differences between the data points and the sinusoidal modal [5]. Typically, least squares estimation methods offer closed-form solutions that are both efficient and robust in estimating amplitude, initial phase, and offset. In the case of frequency, usually an iterative procedure is employed. Traditional methods for amplitude estimation include least squares sine fitting [6], Fourier-based approaches [7], and Bayesian estimation techniques [5]. These methods typically assume the presence of additive noise but often neglect the impact of phase noise and jitter, which introduce correlated distortions affecting amplitude precision. Prior research on sine fitting algorithms [8] has primarily focused on reducing bias and improving convergence but does not explicitly account for the degradation caused by phase noise and jitter. Many measurement techniques rely on sinusoidal signals, where the precision of amplitude estimation directly impacts the overall accuracy of the system. However, real-world measurement systems are subject to noise and imperfections, among which jitter and phase noise are particularly significant. Jitter and phase noise introduce time-domain and frequency-domain distortions, respectively, that can degrade amplitude estimation accuracy. While extensive research has been conducted on the impact of additive noise, the specific contributions of jitter and phase noise to amplitude estimation errors remain less explored. Understanding these effects is critical for designing high-precision measurement systems, improving calibration methods, and mitigating sources of uncertainty in practical applications. This study systematically investigates the influence of jitter and phase noise on the precision of sinusoidal amplitude estimation, providing both theoretical analysis and empirical validation.