How fast fourier transform works on matrix like 3 x 3 matrix

Hello,

I am still learning about how fast fourier transform works on matrix 3 x 3 i want to see how the calculation to get the number at the final it same goes to inverse fourier transform, please help me the matrix example is

1 2 3
4 5 6
7 8 9

Answer 1

[Walter Roberson]

fft() on a 2D matrix is the same as

result = zeros(size(YourMatrix));
for column = 1 : size(YourMatrix,2)
   result(:,column) = fft(YourMatrix(:,column));
end

That is, it just does a column-by-column fft.

fft2() on a 2D matrix is the same as

fft( fft(YourMatrix).' ).'

That is, it does an fft by columns, transposes that so the rows become columns, fft on those columns, and transpose back