Maximum Likelihood Estimation of Band-Limited Power Law Spectrums

Power law spectrums are frequently used to model complex nonlinear systems, with their parameters estimated empirically from measured data. This letter derives a maximum likelihood estimator and Cramér-Rao bound for power law spectrums. An empirical study illustrates that the maximum likelihood estimator outperforms traditional Fourier transform based estimators, and achieves the Cramér-Rao bound. A simple correction to the periodogram linear regression is proposed and is shown to nearly match the maximum likelihood estimator´s performance.