be written as
:

Farid and Simoncelli derivatives

Farid and Simoncelli propose to use a pair of kernels, one for interpolation and another for differentiation (compare to Sobel above). These kernels, of fixed sizes 5 x 5 and 7 x 7, are optimized so that the Fourier transform approximates their correct derivative relationship.

In Matlab code the so called 5-tap filter isk = [0.030320 0.249724 0.439911 0.249724 0.030320];d = [0.104550 0.292315 0.000000 -0.292315 -0.104550];d2 = [0.232905 0.002668 -0.471147 0.002668 0.232905];

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