Realize Partial Pifferention of Convolution in Maltab

Hi everyone,

I'm working on biomedical modeling currently. In the model, I adopted convolution of two functions, i.e. h(x,y) = f(x,y)*g(x,y), where f(x,y) is a stochastic function and g(x,y) is simply x^2+y^2, x,y>0, otherwise, f=0, g=0. Then, I need to calculate dh/dx and dh/dy for next-step modeling.

I have difficulties in doing convolution and partial differentiation when realizing the model in matlab. It seems there are two ways to accomplish the task:

1. use symbolic calculation to get symbolic results and then imply values of the variables to get final result. But the problem is: i). f and g are both discontinuous, so there may be no explicit expression for the integration; ii). I don't know how to express symbolic convolution in matlab;

2. Use numerical calculation, imply vector values to x, and y, then I can get matrix f and g, and then do numerical convolution. The problem is: I don't know how to determine the axis of convolution (since n-vector convolve m-vector yield n+m-1 vector) and how to get accurate dh/dx, dh/dy. I have tried diff(h)./diff(x), but it's time-consuming and the result seems wrong.

I've searched online for many days but without any satisfactory solution. So I'm here looking for help. Any suggestions and comments are welcomed. Thanks a lot.

Q.L