##

Log Bilinear (`module_bilinear.m`)

The log-bilinear transformation for data in the range [-1, 1]
(excluding endpoints) is useful in time-series
analysis for conditioning of the reflection
coefficients (RCs). Although RCs have the nice property of
being fairly uncorrelated, they do have one characteristic
that makes PDF estimation difficult: they tend to be limited to
the region [-1,1]. Thus, the features tend to have a sharp
discontinuities complicating PDF estimation. A simple
nonlinear transformation can improve things dramatically.
The transformation

produces values with a Gaussian-like distribution.
These are called log area ratio (LAR) coefficients [22].
Let the input vector be

contain the zero-lag autocorrelation (ACF) estimate
(i.e. variance) as well as the RCs.
The module
`software/module_bilinear.m` implements the transformation
on . In addition, the module also takes the log of .
The syntax is
[z,jout]=module_bilinear(k,jin);

where variable `k` is the input vector .
Input and output are both of dimension
-by-, where is the number of segments.
The inversion of the LAR coefficients is accomplished by the
`module_bilinear_synth` function.

Baggenstoss
2017-05-19