Constrained least squares estimation of sinusoidal frequencies and application to fast estimation of very low frequency tones

We consider the problem of least squares estimation of the frequency of a single noiseless sinusoidal signal. By constraining the signal model to be an oscillatory system and derive least squares algorithm to estimate the frequency parameters. We extend the solution to the general case of multiple noiseless sinusoids and express the global solution in terms of the inverse of a Toeplitz plus Hankel matrix. We then apply the above algorithm for ultra fast estimation of the frequency of a very low frequency sine wave. Such problems arise in the digital implementations of Ring Tone detectors in automated telephony systems. In high SNR environments, we are able to obtain reasonable estimates of the frequency within a fraction of a single period of the sine wave. We derive expressions for the bias due to additive noise and also experimentally examine the effects of signal distortions.<>