Experimental validation of the precision of sinusoidal amplitude estimation using a least squares procedure in the presence of additive noise

This study focuses on fitting sinusoidal mathematical models to a set of measured data points by minimizing the least squares difference between data points and the model. We investigated the impact of various parameters such as the amplitude, number of data points, and the standard deviation of the additive noise on the sinusoidal amplitude estimation in the specific case where the data points cover an integer number of periods of the sinusoid. The mathematical results are validated by carrying out actual voltage measurements using an analog-to-digital converter. A sinusoidal model with a known frequency, but unknown amplitude, initial phase, and offset is fitted to the acquired samples. The estimated amplitude is consequently a random variable, with its standard deviation influenced by the additive noise standard deviation. The mathematical relation that governs this dependence is presented here and validated experimentally. The resulting analytical expression allows for the computation of confidence intervals for the sinewave amplitude measurements made in the presence of additive noise. Additionally, it provides engineers with a method to determine the number of samples that should be acquired in order to achieve a desired level of precision in the sinusoidal amplitude estimation, or for other quantities derived from the model.