One dimensional solution is in “Expression for discrete fourier transform of linear ramp“

I need two-dimensional for image processing. We have function f(x,y) = $a_1 \cdot x + a_2 \cdot y$,

My experimentatal results:

  • only is one row and one col contains data, all others are empty
  • except [0,0] all real parts in one row are equal
  • similar in one column real parts are equal
  • imaginary parts are descending geometric series for k<N/2

for k = N/2 imaginary is zero, for k > N/2 is mirrored with sign change for k = N/4 imaginary part is is equal real part but sign real part

coefficient geometric series for 8x8 is tangent 22.5 degree but for another sizes are other(unknown way) example 8x8 for f(x,y) = x only first col because all other equal zero, only half rows because lower rows are mirrored


for 12x12

for 8x12

How can we compute this coefficients?

  • $\begingroup$ for 8x8 and 8x12 geometric series is \sqrt(2)+1, in 12x12 is \sqrt(3) $\endgroup$
    – Saku
    Apr 15, 2022 at 15:44

1 Answer 1


Solution: for $N$x$1$ is one dimensional formula, for $N$x$M$ near all coefficients are $M$ times formula, only $[0,0]$ element is another, but this element has their simple formula as average.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.