Figure 9.5 shows the software modules to be discussed and how they relate
to the four equivalent representations of the AR process.
Note that software/module_ar_clt.m can produce either AR or RC depending
on an input flag. There are various means of obtaining
each representation. Most important is that one can obtain ACF
directly from the raw data using software/module_acf_spax.m, or indirectly from the magnitude-squared
Also, various 1:1 modules are provided to convert between the
various representations including software/module_ar2rc.m, software/module_rc2ar.m,
software/module_acf2rc.m, software/module_acf2ar.m, and software/module_rlevinson.m.
Note that in autoregressive analysis, the
prediction error variance (or innovation variance),
, can be derived if one knows the AR coefficients and
the process variance which is the same as the zero-th lag of the ACF, .
Therefore, the two quantities , are interchangeable
when grouped with AR or RC coefficients, or the remaining ACF
coefficients, from an information standpoint.
With both AR and RC, there is a choice of
using either prediction error or variance depending on an input flag.
Depending on the circumstance, one or the other might be more appropriate.
Note that the script software/test_ar.m tests all the modules.
The recommended approach is to use
software/module_acf_spax.m (or software/module_acf_spa.m if intermediate
raw spectrum is needed) followed by the desired conversion module.
The recommended feature type is LAR.
The software modules that perform the conversions are shown.
Relevant sections are software/module_dftmsq.m: Section 4.3, software/module_acf_spa.m: Section 5.2.2,
software/module_acf_clt.m: Section 5.2.5, software/module_ar_ml.m: Section 5.2.8,
software/module_acf2rc.m: Section 9.4.6, software/module_ar2rc.m: Section 9.4.6, software/module_poly2root.m, software/module_root2poly.m: Section 9.4.7, software/module_bilinear.m: Section 4.1.5.
Block Diagram of AR Software Modules
Diagram showing the relationship
of five equivalent representations of an autoregressive
process, autocorrelation function (ACF),
autoregressive coefficients (AR), reflection coefficients
(RC), log area ratio (LAR) coefficients and AR polynomial roots.
It can be verified that any two paths through the figure that end at the same
point will produce the same features and J-function.