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From: oh@m2.csc.ti.com (Stephen Oh)
Newsgroups: comp.dsp
Subject: Re: FFT vs ARMA (was FFTs of Low Frequency Signals (really: decimation))
Message-ID: <99691@ti-csl.csc.ti.com>
Date: 27 Nov 89 15:04:03 GMT
References: <5619@videovax.tv.tek.com> <10208@cadnetix.COM> <2586@irit.oakhill.UUCP> <5305@orca.WV.TEK.COM> <5622@videovax.tv.tek.com> <98204@ti-csl.csc.ti.com> <5630@videovax.tv.tek.com> <98990@ti-csl.csc.ti.com> <1989Nov22.170850.21777@athena.mit.edu>
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Reply-To: oh@m2.UUCP (Stephen Oh)
Organization: TI Computer Science Center, Dallas
Lines: 34

In article <1989Nov22.170850.21777@athena.mit.edu> ashok@atrp.mit.edu (Ashok C. Popat) writes:
>In article <98990@ti-csl.csc.ti.com> oh@m2.UUCP (Stephen Oh) writes:
>>
>>Again, for the resolutions of PSD, parametric approches are *ALOT* better than
>>FFT-based PSD.
>>
>
>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.
>
>Ashok Chhabedia Popat  MIT Rm 36-665  (617) 253-7302


Your assumption is too strong.  You have 10^6 samples with ergodicity?
What if you have 10^6 samples with only wide sense stationary?
What if you have 10^6 smaples with only partially w.s.s?

BTW, I said that parametric approaches are better than FFTs in terms of
resolution. If we have only 100 samples and the separation of two frequencies
is less than 0.01, there is no way to resolve two frequencies using any 
FFT-based method. But AR or ARMA can. :-) :-)
Also, there are several methods to determine the order of the model such as
AIC, MDL, CAT, etc.
+----+----+----+----+----+----+----+----+----+----+----+----+----+
|  Stephen Oh         oh@csc.ti.com     |  Texas Instruments     |
|  Speech and Image Understandung Lab.  | Computer Science Center|
+----+----+----+----+----+----+----+----+----+----+----+----+----+


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