Explicit formula for improved filter sharpening polynomial

A closed-form formula for the extended amplitude change function in filter sharpening is derived. The derivation is based on the Bernstein form representation of the amplitude change function. The function was originally proposed by Hartnett and Boudreaux-Bartels (see ibid., vol.43, p.2805-10, 1995) to achieve better control on amplitude improvement and is a generalization of the Kaiser-Hamming (1977) filter sharpening function.