The estimation of frequency

Abstract

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 θ 0, is in fact 0 or <it is shown that the estimate, , satisfies for N ≧ N 0 (ω) where N 0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.