Talk:Wiener filter

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[edit] Lack of derivation

The article lacks a derivation of the different Wiener filters. --Fredrik Orderud 16:24, 8 May 2005 (UTC)

[edit] discrete time

Hi there. I would like to contribute to this article, specially talking about the discrete time case, solutions, and the LMS and RLS algorithms... But I'm kinda confused, because the way the filter is introduced is different from what I'm used to (what is a good thing, actually).

I believe this article needs some structural changes, but I don't want to simply start changing the place of things and piss off who wrote the current stuff.

I can't say how I think the whole structure of the article should be, because I'm still trying to understand what is there :) . I just would like a place to write specifically about the discrete-time case, with a cross-correlation matrix. Also, I think we should talk about the equalisation case, where the noise is the signal trough a channel, and filtering the noise means finding an inverse filter to the channel!... A hot topic, IMHO. -- NIC1138 05:19, 6 December 2005 (UTC)

[edit] What is S?

In this article what does the capital S stand for?

It is the Laplace transform of small s(t). --Memming 18:30, 2 July 2006 (UTC)
I think S of both types gets a little overused here. In any case diving right into S with double subscripts requires a little explanation (by contrast, R gets defined quite well). As it stands now, the whole solution section is very unclear because of this notation. —Preceding unsigned comment added by 128.30.6.11 (talk) 17:22, 26 October 2007 (UTC)
It is not the Laplace transform of small s(t). It stands for spectral density in the s-domain, which is the Laplace transform of correlation functions for stochastic signals. In this case, Sx,s is the Laplace transform of Rx,s, and Sx is the Laplace transform of Rx.--Yangli2 (talk) 21:58, 10 February 2008 (UTC)

[edit] What is α?

In this article what is the α which suddenly appears in the section entitled stationary solution?

Also I think a discrete time treatment (as mentioned by NIC1138) would be useful. Encyclops 16:27, 13 August 2006 (UTC)

Alpha may be the lead/lag time, which is called d earlier in the article Encyclops 21:45, 13 August 2006 (UTC)

[edit] Isn't there an error in the expected value ?

To avoid making errors in this page and according to my present understanding, I prefer to talk here before doing any modification.

The author wrote : Taking the expected value of the squared error results in

E(e^2) = R_s(0) - 2\int_{-\infty}^{\infty}{g(\tau)R_{x\,s}(\tau + \alpha)\,d\tau} + \int_{-\infty}^{\infty}{\int_{-\infty}^{\infty}{g(\tau)g(\theta)R_x(\tau - \theta)\,d\tau}\,d\theta}

where


but according to Brown and Hwang [1] (page 164), shouldn't it be?


Taking the expected value of the squared error results in

E(e^2) = R_s(0) - 2\int_{-\infty}^{\infty}{g(\tau)R_{s+n\,s}(\tau + \alpha)\,d\tau} + \int_{-\infty}^{\infty}{\int_{-\infty}^{\infty}{g(\tau)g(\theta)R_{s+n}(\tau - \theta)\,d\tau}\,d\theta}

where


s(t) + n(t) doesn't equal x(t)


  • ^ [1]: Brown, Robert Grover and Patrick Y.C. Hwang (1996) Introduction to Random Signals and Applied Kalman Filtering. 3 ed. New York: John Wiley & Sons. ISBN 0-471-12839-2

Touriste 14:14, 25 July 2007 (UTC)

Hmmm! You may have a valid point here. Encyclops 00:30, 27 July 2007 (UTC)

Thanks to Michael Hardy, who didn't write here what he did, the page is now corrected. In fact, the assumptio on uncorrelation between the noise and the signal was forgotten. Touriste 22:29, 21 August 2007 (UTC)

[edit] Yep, I think Touriste is right

I was just looking at the expectation formula, which does not make any sense whatsoever; it needs correction, and I believe Touriste's update is correct. Please, Touriste, overwrite the current formula with your correction next time you log in. I believe the cause of the error is the original author's confusion of the variable names. He must have had multiple sources that used different naming conventions, and in his transcription mismatched them. --Yangli2 (talk) 21:34, 10 February 2008 (UTC)


I just fixed the article; it did follow 2 different naming conventions, the top half, up to just before the expectation formula, used x(t) as the output of the wiener filter, which I replaced with \hat{s}(t); and the bottom half from there on used x(t) as the observed signal, s(t) + n(t). After my replacement, the naming conventions have been reconciled. I added a line of explanation as to what x(t) stands for right after it appears in the expectation formula. --Yangli2 (talk) 22:44, 10 February 2008 (UTC)