The estimation of frequency

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency 0o, is in fact 0 or nt it is shown that the estimate, 0N, satisfies 0N = 0o for N ? No (w) where No (w) is an integer, determined by the realisation, w, of the process, that is almost surely finite.