# Maximum entropy spectral estimation

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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 xi with autocorrelation sequence $R_{xx}(k), k = 0,1, \dots P$ satisfying the constraints:

Rxx(k) = αk

for arbitrary constants αk 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 yi are zero mean, i.i.d. and normally-distributed of finite variance σ2.

## Spectral estimation

Given the ak, 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 xi.

## References

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

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