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Homework Help: Fourier transform matrices

  1. May 2, 2014 #1
    1. The problem statement, all variables and given/known data
    Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F_13 for i, j = 0,1,2, 3.
    Compute F(hat) and verify that F(hat)F = I

    2. Relevant equations
    The matrix F(hat) is called the inverse discrete Fourier transform of F.

    3. The attempt at a solution
    I found that e = 4, so (F)F(hat) = 4 I, so F(1/4 F(hat)) = I
    I calculated that matrix F=
    1 1 1 1
    1 5 12 8
    1 12 8 1
    1 8 1 5

    My Question: How do I calculate matrix F(hat)? I understand it is the inverse of F, but I am unsure of how to calculate it.
  2. jcsd
  3. May 2, 2014 #2


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    Does that mean anything to you? Because it doesn't to me.

  4. May 2, 2014 #3


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    This question should have been a continuation of this thread:


    There the OP said he meant ##5^{i\cdot j}## instead of ##5ij##. Dunno why he didn't correct it for this post.
  5. May 2, 2014 #4


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    Might as well have continued this in your prior post. Now that you have ##F##, the ##i^{th}## row of ##\hat F## has the form:

    $$(1, \omega^{-i}, \omega^{-2i}, ..., \omega^{-(e-1)i})$$

    Where ##\omega## is the e'th primitive root of unity. I'm sure you can continue.
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