Talk:Linear prediction

Autocorrelation matrix form

User 128.125.232.47 made a number of good improvements, but I think there was one mistake. The autocorrelation matrix is very, very rarely a circulant matrix. Indeed, as a speech coding researcher my life would be sooo much easier if it were a circulant matrix:) Anyway, I decided against an immediate revert in order to hear out if there was something I was missing. --Tbackstr 08:40, Jan 11, 2005 (UTC)

On reflection I think you are right here... the Yule Walker equations are not quite circulant though appear to be on first glance.

--Richard Clegg 15:36, 6 Feb 2005 (UTC)

Absolutely correct. The Autocorrelation matrix is not circulant. It is symetric Toeplitz! Also, while the literature frequently ignores the difference between an autocorrelation function and an autocovariance function, what is described here is an autocovariance function. An autocorrelation function is normalized and takes on values between +-1. An autocovariance function is a measure of power.--WLurry (talk) 02:00, 12 February 2008 (UTC)

Well, the symmetry came from the equations, but in real data this doesn't happen because the data is not perfectly AR. Inverse-filtering your signal should give you the lowest-energy possible with a FIR filter, that's what the algorithm guarantees!... We should add some lines about this in the article. -- NIC1138 22:52, 8 December 2005 (UTC)

Urr... shouldn't it be R.a = -r and not R.a = r  ?

This will change the signals of the vector a. It depends if you want directly the coefficients of the filter or the coefficients of the polynomial in the z space. -- NIC1138 22:52, 8 December 2005 (UTC)

Subscripts versus function notation

Is there a good reason for using function notation ${\hat {x}}(n)$, $\ x(n-i)$ instead of subscripts ${\hat {x}}_{n}$, $\ x_{n-i}$? I think subscripts would be clearer, but I'm not positively sure that the original editor didn't have a good reason not to use subscripts. Discussion? --Quuxplusone 04:09, 17 August 2005 (UTC)

I like even more Oppenheim's square bracket notation, ${\hat {x}}[n]$, ${\hat {x}}[n-k]$. But perhaps I'm too much of a C programmer... I would vote for subscript.

And a related subject: I'm going to change "digital signal" for "discrete-time" signal, following again Oppenheimistic tendencies. :) -- NIC1138 20:51, 7 December 2005 (UTC)

Changed notation in a formula

I changed this formula:

$\ R(i)=E\{x(n)x(n-i)\}\,$

To this:

$\ R(i)=\sum _{n}x(n)x(n-i)\,$

since I think that's what was meant (it's describing an autocorrelation, and a sum would be used here). I'm not familiar with the notation in the first version; somebody correct me if my change was wrong. - furrykef (Talk at me) 17:34, 12 April 2006 (UTC)

The expectation notation is probably better -- I have added a link to expectation for those not familiar. --Richard Clegg 17:48, 12 April 2006 (UTC)

You're sure that's correct? I'm not sure I see the connection with expected value, but I'm probably just a n00b. - furrykef (Talk at me) 18:18, 12 April 2006 (UTC)

Checkout the page on autocorrelation. There are lots of definitions for ACF (they are all related but not the same). The one given here is not my preferred definition but it is better than the summation. --Richard Clegg 18:46, 12 April 2006 (UTC)

Filter theory

There is a wikilink in this article to filter theory which is actually a redirect. It used to go to digital filter but I have changed it to point to filter (signal processing) which makes much more sense to me. If this article really needs the link to go to "digital filter" a pipe could always be used. Ideally of course, someone should write an article at "filter theory".... SpinningSpark 23:43, 27 August 2009 (UTC)