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Digital signal processing - Pseudo Inverse Method

  1. Feb 7, 2014 #1
    Digital signal processing -- Pseudo Inverse Method

    1. The problem statement, all variables and given/known data
    IMG_1799_zpsb54d4610.jpg


    3. The attempt at a solution

    (a)

    A =the matrix with [ .4 0 0 0 0 0 0 0 0 0 0 0; .7 .4 0 0 0 0 0 0 0 0 0; -.1 .7 .4 0 0 0 0 0 0 0 0;..... all the way down to 0 0 0 0 0 0 0 0 0 0 -.1] so it is 11 x9 .
    w=[w0 w1 ... w8]' d0 = [1 0 0 0 0 0 0 0 0 0 0] .... to d10 = [ 0 0 0 0 0 0 0 0 0 0 1]

    A'Aw=A'd and w=(A'A)^-1 A'd so dhat = A(A'A)^-1 A' d

    do E = || d -dhat || ^2

    So to get the optimum delay dn I calculate dhat_n = A(A'A)^-1 A' d for 0,1,2,3...10
    and get E_n = || d_n - dhat_n ||^2 for each n and find which one gives the minimum?

    I get a curve that is not concave when I do this. Shouldn't it be a concave up curve and not a decaying function? I am not sure what I did wrong and the entire problem relies on this part.
     
  2. jcsd
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