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Basic 2d DFT - interpreting the coefficients! please help

  1. Jan 9, 2012 #1
    Thanks for any help! I'm trying to understand the coefficients of a 2d DFT.

    say we've got this matrix, f(a,b)

    [itex]
    \left( \begin{array}{ccc}
    9 & 1 & 9 \\
    9 & 1 & 9 \\
    9 & 1 & 9 \end{array} \right)
    [/itex]

    I used wolfram alpha's function, Fourier{f(a,b)}
    and the transform comes back as

    [itex]
    \left( \begin{array}{ccc}
    19 & 4-6.93i & 4+6.93i \\
    0 & 0 & 0 \\
    0 & 0 & 0 \end{array} \right)
    [/itex]


    the characteristic polynomial is [itex] 19x^{2} - x^{3} [/itex]


    I know the coeffecient at (0,0) is an average of something, but what?
    what are the other two coefficients in the top row?

    If I do a matrix with a frequency in both directions, I get coefficients in the first column as well. What do they represent?

    Is there enough information here to determine a function z(x,y) that approximates f(a,b)? (like a sum of sines and cosines)

    three eigenvectors are given as well, if needed

    thanks for your help!
     
  2. jcsd
  3. Jan 9, 2012 #2
    Would a moderator move this to the calculus section please? 126 views and no responses yet :(

    thanks
     
  4. Jan 9, 2012 #3
  5. Jan 9, 2012 #4
    I checked it out, but I don't think it answers my questions. At least not in a way that I comprehend.

    How are the coefficients related to frequencies?
     
  6. Jan 10, 2012 #5
    The 1-D DFT is the dot product of the signal with a vector containing a complex sinusoid which oscillates over the indices at a variable frequency, according to the given formula.

    http://reference.wolfram.com/mathematica/ref/Files/Fourier.en/3.gif [Broken]

    If s was 1, we'd get the zero frequency because s-1 = 0 and e^(2∏i0) = 1 (a constant).

    We haven't defined a sampling rate. So, I suppose I could call (s-1) the frequency. Since (r-1)/n would be from 0 to (n-1)/n (evenly spaced sampling in the interval 0 to 1), the number of oscillations of the complex sinusoid from r = 1 to n is the oscillations of a sinusoid with frequency (s-1) over a domain of length one.
     
    Last edited by a moderator: May 5, 2017
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