Omnidirectional plane-wave destruction

Additional constraint

The above maxflat condition is a linear system with $(2N+1)^2$ unknown variables $f_{k_1k_2}$ . In order to obtain a non-zero solution, we use only the first $4N^2+4N$ equations, which zeros the partial derivatives with order less than $(2N+1)^2$ , and impose an additional constraint on the filter coefficients,

$$\sum_{k_1=-N}^N\sum_{k_2=-N}^Nf_{k_1k_2}=1.$$ (13)

This additional constraint yields a unit amplitude response at zero frequency, similarly to the 1D maxflat approximation (Chen et al., 2013).