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.
Log Bilinear (module_bilinear.m)
produces values with a Gaussian-like distribution.
These are called log area ratio (LAR) coefficients .
Let the input vector be
contain the zero-lag autocorrelation (ACF) estimate
(i.e. variance) as well as the RCs.
software/module_bilinear.m implements the transformation
on . In addition, the module also takes the log of .
The syntax is
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