I guess it's easier to use an analogy to understand the problem. Imagine throwing a rock to water and we see the waves propagating. Assume that we recorded the amplitude of the water waves of all grid points in one second (it would be a 3D matrix where the dimensions 1 and 2 are coordinates X, Y; and the third dimension is amplitude in time). And I want to further extrapolate the waves in time, it must be the waves goes further and further.
My problem is I don't have a good approach of how to do this, not just the detail of the MATLAB code.
- I tried to use AR model for all points to extrapolate further in time, however, it cannot extrapolate in space (means that the waves does not propagate further).
- I tried another way, which was to transform the data to frequency domain using function fftn. Then interpolate data in frequency domain and transform back to time domain. The result is that the waves repeat again, not propagating further as I wanted.
Any help will be appreciated. Many thanks, Truong.
