I should be able to generate a stationary GRF from white noise in two different ways:
- multiplying the white noise vector by the square root of a covariance matrix with appropriate kernel;
- taking the 2D convolution of the white noise field with a 2D kernel
Each of these methods uses a kernel, but using the same kernel for both doesn't give samples from the same GRF.
If I want to use the convolution method to sample from the same GRF as the matrix method, how do I calculate the convolution kernel from the matrix kernel?
I would guess that I should take the square root of the matrix kernel, is this right?