For a small number of sinusiods, the total number of
parameters for the SINAR model is small, so
the feature PDF can be approximated by Gaussian mixtures, etc.
The function
`software/module_sinar_test.m` implements
the acid using Gaussian mixtures test with `method='gmm'`.
However, for more sinusoids, a PDF estimation method
more suited for SINAR should be used.
The fixed parameters for the SINAR
model of AR order and sinusoids
include the AR parameter estimates
,
,
the vector of frequencies ,
and the -dimensional vector of
real and imaginary amplitudes .
Let be an arbitrary (real data) hypothesis
and assume we want to estimate
.
We make the simplifying assumption that
the AR and sinusoidal parameters are independent:

If we expand

we can implement
as a histogram.
If we assume the individual frequencies are independent,
we have

where is the frequency histogram for class .
In addition, we can assume a standard exponential distribution for the
squared magnitudes,

where can be constant or can depend on the frequency.
In the second case, a means of estimating
should be used.
These ideas are implemented by the function
`software/spect_hist.m`.
The function
`software/module_sinar_test.m` implements
the acid using histogram with `method='hist'`.

Baggenstoss
2017-05-19