Constrained least squares estimation of sinusoidal frequencies and application to time frequency analysis of chirp signals

In this paper, we consider the problem of least squares estimation of the frequency of a single noiseless sinusoidal signal and derive a least squares algorithm to estimate the frequency parameters. We show the effects of adding noise to the signal. Secondly, we propose two adaptive versions of the algorithm and apply them to determine the instantaneous frequency of a modulated tone. We illustrate results by several chirp signals. By adding mild amounts of noise, we show that the algorithm is fairly robust. We feel that the computational simplicity of this algorithm makes it a competitive alternative to the modern time frequency signal analysis methods for monocomponent signals