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From: oh@m2.csc.ti.com (Stephen Oh)
Newsgroups: comp.dsp
Subject: Re: FFTs of Low Frequency Signals (really: decimation)
Message-ID: <98204@ti-csl.csc.ti.com>
Date: 14 Nov 89 19:43:36 GMT
References: <5619@videovax.tv.tek.com> <10208@cadnetix.COM> <2586@irit.oakhill.UUCP> <5305@orca.WV.TEK.COM> <5622@videovax.tv.tek.com>
Sender: news@ti-csl.csc.ti.com
Reply-To: oh@m2.UUCP (Stephen Oh)
Organization: TI Computer Science Center, Dallas
Lines: 36

In article <5622@videovax.tv.tek.com> bart@videovax.tv.tek.com (Bart Massey) writes:
>
>Or, as I said in my original posting, ARMA estimators are certainly better
>than DFTs at picking a single sinusoid out of white noise, regardless of the
>ratio of input frequency to sample rate, and regardless of record length.
>The chief disadvantages of using this class of techiques over the FFT are
>that (1) they may be more computationally expensive than an FFT, and (2)
>they make stronger assumptions about the form of their input than the FFT,
>and thus tend to give wrong or misleading answers in cases of unexpected
>input.

I agree with Bart that ARMA estimators are better than FFTs. However, I don't
see any reason (expect one, I will discuss about this later) why we should use
ARMA estimators instead of AR estimators. If you want to pick sinusoids out of
white noise with moderate computations,  you should use AR estimators.
(For sinusoid estimation, the MLE of sinuoids (direct parametric approach) is
the best in term of performance, but it requires HEAVY computations.) The
main advantages over ARMAs is computational expensive. There are *lots* of
techniques available. Please refer to Marple and Kay's books.
If you want to pick deep valleyes (instead of peaks) from PSD, 
definitely you should use ARMA instead AR.

One more comment: 
      In order to improve the statistical stability of FFTs,
      it is very common to use psuedo ensemble average by segments of data.
      This causes the reduction of resolutions of PSD.
      So if you want to increase the resolution as well as to improve the
      stability, you need *lots* of computations. Because of this fact, I
      don't think that AR estimators are computationally more expensive
      than FFTs.


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|  Stephen Oh         oh@csc.ti.com     |  Texas Instruments     |
|  Speech and Image Understandung Lab.  | Computer Science Center|
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