I am trying to use the Hadamard transform on a delta function to generate Hadamard patterns as shown below.

$$tag{4} P_Hleft(x,yright)=frac{1}{2}left(1+H^{-1}left{delta _Hleft(u,vright)right}right)$$

Where $H^{-1}left{right}$ denote an inverse Hadamard transform and

$$tag{5}delta _Hleft(u,vright)=begin{cases}1, space u=u_0, v=v_0\0,space text{otherwise}

end{cases}$$

However, I am not sure what the delta function is supposed to do. Could anyone show me a simple example with real values of x,y,u, and v so that I can learn what to do?