Performance comparison of the three-parameter and the four-parameter sine-fit algorithms

The aim of this paper is to compare the performances of the three-parameter sine-fit (3PSF) and the four-parameter sine-fit (4PSF) algorithm when a sine wave corrupted by a Gaussian noise is analyzed. Algorithm accuracy is evaluated by means of the expected sum-squared fit error and the normalized frequency required by the 3PSF algorithm is estimated by the Interpolated Discrete Fourier Transform (IpDFT) method. It is shown that the 4PSF algorithm produces a somewhat better fit than the 3PSF algorithm, but the achieved accuracies are almost equal when the number of acquired samples is greater than 512. The theoretical expressions derived in the paper are confirmed by means of both computer simulations and experimental results.