Minimum Fisher information spectral analysis

Minimizing the Fisher informationmeasure over the set of power spectrum densities tting a nite number of autocorrelation lag constraints is treated. Due to an explicit control of the derivative values of the densities, the Fisher information measure produces a useful smoothing e ect. The Fisher informationbased estimate exhibits improved characteristics compared to the maximum entropy approach proposed by Burg. We show that the resulting power spectrum estimate is positive, and along with the autocorrelation constraints, satis es a generalized Riccati di erential equation. In general, the true estimate of the power spectrum may be obtained only by numerically integrating the corresponding boundary value problem. For real time applications, we therefore propose a fast and numerically stable approximate solution in explicit trigonometric form. Although suboptimal, the proposed approach has proven to be advantageous especially for at spectra. The presented theory is veri ed on simulated examples.