Thanks for any help! I'm trying to understand the coefficients of a 2d DFT.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Basic 2d DFT - interpreting the coefficients! please help

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