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 frequencyθ₀, is in fact 0 or N≧N₀(ω) whereN₀(ω) is an integer, determined by the realisation,ω, of the process, that is almost surely finite.