I have data that form a scalar field on a 2D grid, evenly spaced. The grid has a finite size. There is no particular periodicity patern in my data.
I want to calculate the value of the gradient at each grid point with a spectral method in MATLAB. Using simple FFT does not seem to work, especially near the borders (probably because the data are not periodic). I have ears about DCT, but I am not sure.
I would appreciate advice on the best way to do this.
Edit : I think that I could extend my grid with one row/column at each of the 4 boundaries, duplicate the real boundary on these new boundary points to get a zero derivative boundary for the DCT algorithm. However, I am not sure how to get it working. Another possibility would be to extend my grid in some way that FFT will not create spurious oscillation near the boundaries, but again, I my attempts failed so far.