CONTINUOUSLY VARIABLE PEF'S

Inevitably, we get involved with nonstationarity and we become interested in continuously variable PEF's. Again, 1-D theory guides us. We can do regional averaging of c's and that preserves minimum phase. Likewise, we can independently average across micropatches the numerator and denominator of (2). Many people did this in the old days when filter theory was basically one dimensional.

Polynomial division by nonstationary PEFs made up from an assemblage of stationary ones need not, however, be necessarily stable, as shown by Rickett (1999). He demonstrated instability when two stable PEFs alternated at alternate time points. Whether this kind of instability would arise in practice remains to be seen.