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:

$R_{xx}(k) = \alpha_k$

for arbitrary constants $\alpha_k$ 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 $\sigma^2$.

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.