Diriehlet Apodization

Dirichlet apodization is perhaps the laziest approach, since the window of total width Wis simply an enlarged version of ft0, which requires no more computational effort than a test to indicate support membership. The apodized synthesis function is given by

where Wis an even integer. The price to pay for laziness is bad quality. First, the regularity of this function is low since it is not differentiable. More important, its approximation order is as bad as L = 0, and this function does not even satisfy the partition of unity. This means that a reduction of the sampling step does not necessarily result in a reduction of the interpolation error. Instead of Eq. (11), we have that

0 0

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