Hann and Hamming

This family of interpolation kernels are defined from the same function, namely:

$$H(x) = \left\{ \begin{array}{ll} \alpha + (1 - \alpha) \cos( ... ...rt<\frac{N-1}{2} \\ 0 & \mbox{otherwise} \end{array} \right.$$

where N is the number of samples in the windowing function. The two functions differ in the choice of $\alpha$. For Hann, $\alpha=1/2$ and for Hamming, $\alpha = 0.54$.

Figure 8 shows both kernels. They have the interesting property of always being positive, which limits the Gibbs phenomenon in edge neighbourhoods. Notice that the Hamming kernel is discontinuous. These kernels are widely used in electronics for digital filter design, more information can be found about them in any book related to digital signal processing.

  

Figure 8: Hann and Hamming kernels