Just as linear shift-invariant systems and rational transfer models are central to classical signal processing, stationary signals and Toeplitz covariance matrix models are central to statistical signal processing. An extensive selection of routines is provided for solving fundamental statistical signal processing problems.

The PV‑WAVE Signal Processing Toolkit provides a complete suite of routines for manipulating Toeplitz matrix equations: the JURYRC, LEVCORR and LEVDURB procedures, and the TOEPSOL function. These routines and the other various statistical signal processing functions are summarized in Table 1-9: Statistical Signal Processing Routines. For more detailed information, see Chapter 2: Reference (A to F), Chapter 3: Reference (G to P), and Chapter 4: Reference (Q to Z).

The optimal linear phase FIR Wiener filter design problem is solved using the FIRLS function. A connection between the transfer function models of classical signal processing and the stationary random signal models of statistical signal processing is provided by Prony’s method which is part of the IIRLS function.

The most important signals in theoretical statistical signal processing are normal random variables and quadratic forms of normal random variables. The PV‑WAVE Advantage RANDOM and RANDOMOPT functions provide the basic tools for generating such random variables. The PV‑WAVE Advantage reference pages for these routines are reproduced in this manual for your convenience.