###### Abstract
By quantifying their impact on residuals in sine fitting, we aim to offer insights that will aid researchers and engineers in improving measurement reliability in metrology, communications, and sensor applications. In real-world applications, the signals that would ideally be sinusoidal are affected by a myriad of phenomena that distort it in different ways. Examples of these are the non-linear behavior of systems and devices that introduce extra additive sinusoidal components with different frequencies, additive random noise [9], usually normally distributed, quantization error, introduced by the use of analog-to-digital converters with a finite number of bits, phase noise in the signal generators, and uncertainty in the sampling instant, to name just a few. All those non-ideal phenomena affect the metrological characteristics of the sinewave parameter estimation (bias and precision) and of those quantities that are derived from them like gain, bandwidth, total harmonic distortion, and signal-to-noise ratio. The work presented here deals specifically with the estimation of sinewave amplitude obtained from data points sampled from real signals where the sampling process is affected by jitter, which is random, normally distributed with null mean and known standard deviation. Despite extensive research on signal estimation techniques, including the thorough treatment of estimation theory by [PERSON] [5] on the impact of jitter on digital systems [10; 11], there remains a need for comprehensive studies that analytically and experimentally address the impact of sampling jitter on sinusoidal amplitude estimation. As one would expect, such an important estimation has been the subject of previous publications. In 1987, [PERSON] studied the effect of ADC quantization errors on some periodic signal measurements, including sinusoidal amplitude [12]. More specifically, the effect of sampling jitter, which is the subject of this work, has been studied by the same author, together with [PERSON] in [13]. It derived an approximate analytical expression for the variance of sinusoidal amplitude estimation as a function of jitter variance. Furthermore, it presented the results of numerical simulations intended to validate the analytical derivations. Those results showed a discrepancy between the theoretical and the simulation values, which can be clearly observed in Figure 5 of [13]. The authors acknowledge this discrepancy, which happens also in the case of the estimation of the initial phase of the sinusoid, by saying in the last paragraph before the conclusions: \"Both figures show a noticeable systematic deviation between the theoretical results and simulations. The authors could not determine the reason for such deviation\". It is exactly this deviation that was the driving force behind this paper. The author felt that this warranted further investigation to understand the cause of the discrepancy or, at least, confirm that there was one. This was performed here, not only using numerical simulation but also experimental data obtained from actual sampled data points intentionally corrupted by a controllable amount of jitter. Anticipating what comes next in this work, it will be shown that the analytical derivation is correct and that new data from numerical simulation do indeed agree with that expression. Note that this was tried with different numbers of samples and that even with the low number of samples used [10], just 32, there was no discrepancy. Since the original paper [10] did not supply details regarding the numerical simulation procedure used, it is impossible to pinpoint what went wrong there. Furthermore, the experimental data presented here are also in accordance with the analytical expression. Note that, naturally, the author tried to find another publication where the subject of least squares sinusoidal amplitude estimation in the presence of jitter was addressed. Only one such publication was found, namely one from [PERSON], [PERSON], and [PERSON] in 1994 [14].