Maximum entropy spectral estimation
Encyclopedia
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.
with autocorrelation
sequence
satisfying the constraints:
for arbitrary constants
is the 
-th order, linear Markov chain of the form:
where the
are zero mean, i.i.d. and normally-distributed of finite variance 
.
, 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
.
Spectral density estimation
In statistical signal processing, the goal of spectral density estimation is to estimate the spectral density of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal...
. The overall idea is that the maximum entropy rate
Entropy rate
In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process...
stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
that satisfies the given constant autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
and variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
constraints, is a linear Gauss-Markov process with i.i.d. zero-mean, Gaussian input.
Method description
The maximum entropy rate, strongly stationary stochastic processStochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
with autocorrelationAutocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
sequence
satisfying the constraints:for arbitrary constants
is the -th order, linear Markov chain of the form:where the
are zero mean, i.i.d. and normally-distributed of finite variance .Spectral estimation
Given the, the square of the absolute value of the transfer functionTransfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...
of the linear Markov chain model can be evaluated at any required frequency in order to find the power spectrum of
.External links
- kSpectra Toolkit for Mac OS X from SpectraWorks.