Computing the frequency of a sampled sinusoidal function

This paper deals with the problem of evaluating the frequency F of a sinusoidal function y(x), given N samples yi, i equals 1,2,. . . ,N, that represent values of y(x) affected by errors epsilon //i having a Gaussian distribution. The samples are uniformly spaced at intervals DELTA x. For this purpose an algorithm is proposed that requires at most 4N additions and 2 divisions to be performed. The error epsilon //f affecting F has been estimated by simulation. It has been found that epsilon //f has quite a Gaussian distribution (for N greater than 10), and, if the standard deviation of the errors epsilon //i is less than 25% of the amplitude of y(x), than the mean and the standard deviation of epsilon //f are only a few percent of the maximum value of F, i. e. , of Fmax equals 1/(2 DELTA x).