Maximum entropy techniques can be useful in speech processing applications, where the goal is to reconstruct intelligible speech from signal data.
Many spectral analysis techniques start with measured values of the autocorrelation function of a signal at a set of points. One class of techniques proceeds by extrapolating to reasonable values at the unknown points. The extrapolated autocorrelation function is equivalent to a power spectrum estimate, since the power spectrum of a bandlimited stationary process is related to its autocorrelation function by a Fourier transform.
Perhaps the best known extrapolation technique is Burg's, in which the power spectrum is estimated by maximizing:
subject to the constraints
where W is the bandwidth and where , are known value of the autocorrelation function.
With a numerical method (e.g., Newton's method), the solution to the above problem can be found using standard techniques. Using this solution, it is then possible to extrapolate the autocorrelation function arbitrarily. A reasonable approximation to the original signal can then be made.
For further information about spectral analysis, and a comparison of the burg and boltzmann-shannon entropies, consult . Our work involves extending these comparisons to more entropy types and to different applications.
A Comparison of Entropies in the Underdetermined Moment Problem