🚀 go-pugleaf

In article <1989Nov22.170850.21777@athena.mit.edu>, ashok@atrp.mit.edu (Ashok
C. Popat) writes: 
> In applications, you don't always have a good apriori formal model.
> Unless you have a formal model that's *useful* for your application,
> parametric estimation is worthless.
> 
> Suppose I gave you some data (say 10^6 samples) and told you that the
> source was ergodic, but nothing else.  How would you estimate the
> spectrum?  If you used an ARMA model, how would you decide what the
> order of the model should be?  Wouldn't you have much more confidence
> in an averaged-periodogram (i.e., DFT-based) estimate?  I would.

Nor necessarily.  DFT is quite good at some things, not at others.  If you
give me recorded data that I can play with for a while, I would probably run
FFT, several different periodograms, ARMA or Prony models of several orders
and whatever alse the data made me feel like.  After doing all that, I'd feel
reasonably confident I could tell you something about your data.

If averaged periodograms showed different behavior in different segments of
the data, that means you also want to look at parametric models over subsets
of the data.

In short, if I knew that little no ONE technique would make me happy.  And
finally, the fact that the DFT is non-parametric does not mean that you aren't
making assumptions about the data (in fact, you're assuming periodicity --
something that doesn't always make sense either)

SR
"But the real reason is, I just like to play."