Example: focusing a point source
With global strategy, we design the filters in such a way that the response of the system is a Dirac’s delta function for source K, and is zero for all the other P-1 source positions. So we set up a linear equation system of P equations, imposing that:
Lets call vk the right-hand vector of known results. Once this matrix of N inverse filters are computed (for example, employing the Nelson/Kirkeby method), the output of the microphone array, focused on the K point source, will again be simply: