(newbie) spectral derivative

I have data that form a scalar field on a 2D grid, evenly spaced. 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.

[Jack Silver]

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.

[Sean de Wolski]

Why not just use gradient?

[Jack Silver]

Thanks, for your answer, but my understanding is that the "gradient" function is based on finite difference, which is not accurate enough for my needs.

I would definitly prefer a spectral solution.