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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,

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

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