Talk:Prony's method

Latest comment: 4 years ago by Redav in topic Error regarding minus signs

How is it that there are only N samples for F(n) whereas the matrix equation makes use of F from 0 to 2N-1? Bsofly 16:47, 4 December 2006 (UTC)Reply

Formulation is clearly wrong. —Preceding unsigned comment added by 130.203.193.252 (talk) 19:05, 10 October 2007 (UTC)Reply

The formulation is correct. See Eq. 11 of the citation [1]. --Chassin (talk) 19:01, 10 October 2010 (UTC)Reply

Error regarding minus signs

edit

In the article I read:

"Because the summation of complex exponentials is the homogeneous solution to a linear difference equation, the following difference equation will exist:

 

The key to Prony's Method is that the coefficients in the difference equation are related to the following polynomial:

 "

Considering the single-mode situation, where:

 

we clearly have:

 .

Transforming this into a difference equation (whether or not this is the same as Z-transforming, I am not completely sure, but I am more or less following from the article), we get:

 .

But this difference equation, according to the notation of the second equation quoted from the article, corresponds to:

 ,

with a minus sign in front of  , so we can identify:

 .

Substituting this into the first equation quoted from the article, as it is until now, with  , yields:

 ,

which clearly contradicts the second equation derived by me.

I conclude that the minus sign on the right-hand side of the first equation quoted above is erroneous, and that a similar flaw is present in the first matrix-vector equation in the article, as it is until now. I will therefore correct these errors shortly.Redav (talk) 17:30, 28 June 2020 (UTC)Reply