Minimum Fisher information spectral analysis

Minimizing the Fisher information measure over the set of power spectrum densities fitting a finite 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 effect. The Fisher information based estimate exhibits improved characteristics compared to the maximum entropy approach proposed by Burg (1967). We show that the resulting power spectrum estimate is positive, and along with the autocorrelation constraints, satisfies a generalized Riccati differential 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 flat spectra. The presented theory is verified on simulated examples.