RECURSIVE AUTOREGRESSIVE SPECTRAL ESTIMATION BY MINIMIZATION OF THE FREE-ENERGY

We have developed a new digital signal processing technique applicable to power spectrum estimation designated as the minimum free energy method. With no a priori model assumption and no attempt to extract special features such as sinusoids, we are able to obtain high resolution even with high noise contamination of the measured signal. In this study we have chosen to demonstrate the minimum free energy technique by modification of the Burg recursive method of spectral analysis. Burg's method borrows the efficient Levinson algorithm of the maximum entropy method but avoids the difficulty of estimating the autocorrelation sequence. Burg chooses the reflection coefficient to minimize the sum of forward and backward prediction error energies. We propose a recursive minimum free energy method in which we choose the reflection coefficient at each step to minimize the free energy (the Burg energy measure minus the product of a temperature and an information entropy). Our novel innovation produces a spectral estimator more impervious to high noise contamination than the Burg method and diminishes the Burg tendency to produce spurious peaks.