1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wiener Filter, Correlation Matrices

  1. Feb 21, 2010 #1
    I'm trying to understand the Wiener Filter, and I have a few questions.

    1. How can there be such a thing as a correlation matrix of 1 vector. I read here:

    R_yy = E[ y(k) * y^T(k) ]

    where y(k) is a vector, and y_T(x) is the same vector transposed. I thought correlation represents the degree of correspondence between 2 variables, so how can we say there is a correlation between 2 equivalent vectors?

    2. They present a matrix R_yy as the correlation matrix (mentioned above). Then they say vector "r_yy" is the first column of R_yy. If that is so, what are the other columns of R_yy?

    3. The book first presents the Wiener filter formulation by saying that in minimizing the MSE criterion, we can find "h_w" (the wiener filter vector). They go on to another form of the Wiener filter by saying:

    h_w = h_1 - inv(R_yy)*r_vv

    where h_1 was defined as [1 0 0 0 ...]^T and r_vv, I suppose is the correlation (once again I dont know how one can have correlation between 2 equivalent vectors).



    Thank you for any help.
     
  2. jcsd
  3. Feb 24, 2010 #2
    Any ideas?
     
  4. Feb 24, 2010 #3
    ryy is the auto-correlation, witch you can think of as the correlation between the signal and shifted versions of itself. The relationship posted by you is actually ryy(0).
    ryy(n)= E{y(k)*yT(k-n)}
    That matrix is a symmetric toeplitz matrix. Indeed the first column is ryy, the second is [ryy(1) ryy(0) ryy(1) ryy(2) ... ryy(N-1)]T and so on the last one is ryy reversed.
    I don't quite understand what you mean by your notation here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Wiener Filter, Correlation Matrices
  1. The Matrices (Replies: 12)

  2. Notch filter (Replies: 22)

Loading...