BIAS OF TRIANGULAR SIGNAL AMPLITUDE ESTIMATION USING THREE-PARAMETER SINE FITTING IN THE PRESENCE OF ADDITIVE NOISE

Triangular waveforms are widely used as stimulus signals in instrumentation and measurement, and their amplitude is frequently recovered by applying a least-squares sine-fitting algorithm to the signal’s Fourier fundamental. This paper examines the accuracy of that approach when the acquired samples are corrupted by additive Gaussian noise. Because the three-parameter sine-fit estimator is non-linear in the amplitude, the recovered value is systematically biased — a behaviour that, for a triangular input, does not appear to have been quantified before. A compact approximate expression is derived for the relative amplitude error in terms of the signal amplitude, the noise standard deviation and the number of acquired samples. It shows that the bias, though never exactly zero for a finite record, diminishes as the number of samples grows and vanishes in the limit, so that the estimator is asymptotically unbiased. The expression is confirmed by both Monte Carlo simulation and measurements on a data-acquisition system, and it allows a confidence interval to be assigned to triangular-amplitude measurements or, when the noise level is known, the bias to be corrected. Only the three-parameter algorithm under coherent sampling is considered.