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.
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机译:我们考虑一个最小二乘估计单个无噪声正弦信号的频率的问题。通过将信号模型约束为振荡系统并导出最小二乘算法来估计频率参数。我们将解决方案扩展到多个无噪声正弦曲线的一般情况下,并在Toeplitz Plus Hankel矩阵的逆方面表达全球解决方案。然后,我们将上述算法应用于非常低频正弦波的频率的超快速估计。自动电话系统中的铃声探测器的数字实现中出现了这些问题。在高SNR环境中,我们能够在正弦波的单个周期的一小部分内获得合理的频率估计。由于附加噪声,我们派生偏差的表达,并通过实验检查信号扭曲的影响。
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