Maximum entropy spectral estimation

The maximum entropy method applied to spectral density estimation. The overall idea is that the maximum entropy rate stochastic process that satisfies the given constant autocorrelation and variance constraints, is a linear Gauss-Markov process with i.i.d. zero-mean, Gaussian input.

Method description

The maximum entropy rate, strongly stationary stochastic process x_i with autocorrelation sequence $R_{xx}(k), k = 0,1, \dots P$ satisfying the constraints:

R_xx(k) = α_k

for arbitrary constants α_k is the P-th order, linear Markov chain of the form:

$x_i = -\sum_{k=1}^P a_k x_{i-k} + y_i$

where the y_i are zero mean, i.i.d. and normally-distributed of finite variance σ².

Spectral estimation

Given the a_k, the square of the absolute value of the transfer function of the linear Markov chain model can be evaluated at any required frequency in order to find the power spectrum of x_i.

References

• Cover, T. and Thomas, J. (1991) Elements of Information Theory, John Wiley and Sons, Inc.

External links

• kSpectra Toolkit for Mac OS X from SpectraWorks.