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Finding the inverse matrix of fourier transform

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data

    If y=(1,0,0,0) and F4*c=y, find c.

    2. Relevant equations

    c=F4-1*y

    3. The attempt at a solution

    I'm stuck. I don't know how to get F4-1.

    F4-1 = (1/N) * [1, 1, 1, 1; 1 -i (-i)^2 (-i)^3; 1 (-i)^2 (-i)^4 (-i)^6; 1 (-i)^3 (-i)^6 (-i)^9] (this is a 4x4 matrix)

    N = 4

    So I'm confused because from that I get,

    (1/4)* [1 1 1 1; 1 -i -1 i; 1 -1 1 -1; 1 i -1 -i]
    (this is a 4x4 matrix)

    I know that after I get this matrix, I just have to multiply by y to get c, but that inverse matrix has me confused.

    Can anyone please help??? Thanks!
     
    Last edited by a moderator: Oct 16, 2011
  2. jcsd
  3. Oct 16, 2011 #2

    Mark44

    Staff: Mentor

    Is what you have in the brackets above F4?
    If so, use it to find the inverse, F4-1.
     
  4. Oct 16, 2011 #3
    I do not have F4... What I'm showing is what I've worked so far for inverse of F4...
     
  5. Oct 16, 2011 #4
    I figured this out... I was actually doing it right and the inverse is that matrix I specified with the i's in it. The i's were throwing me off, but when you multiply that matrix by y, the i's cancel out and you can find c. :-)
     
  6. Oct 16, 2011 #5

    Mark44

    Staff: Mentor

    Your first post was not very clear on what you were given. Apparently you are given F4-1, so there's no need to find F4.
    and you simplified it to get
    F4-1 = (1/4)* [1 1 1 1; 1 -i -1 i; 1 -1 1 -1; 1 i -1 -i][/quote]
    You know y, and you have worked out that c = F4-1y, so just carry out the multiplication of your matrix and y.

    [tex]c = \frac{1}{4}\begin{bmatrix}1&1&1&1\\1&-i&-1&i\\1&-1&1&-1\\1&i&-1&-1\end{bmatrix} \begin{bmatrix}1\\0\\0\\0\end{bmatrix}[/tex]
     
  7. Oct 16, 2011 #6
    Thank you!
     
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