Interpolation Kernels

In this section the available kernels are defined. See also [10]. The KNAB interpolation kernel is described in a IEEE letter of 2003. The Raised Cosine interpolation kernel is described in a article in J. Of electromagnetic waves, 2005. Cho et al.

$$sinc(x) = {\sin\pi x \over \pi x}$$ (U3)

$$rect(x) = \left\{ \begin{array}{ll} 0 & \vert x \vert > 0.5 \\ 0.5 & \vert x \vert = 0.5 \\ 1 & \vert x \vert < 0.5 \\ \end{array} \right.$$ (U4)

$$i(x) = tri(x) = \left\{ \begin{array}{ll} 0 & \vert x \vert > 1 \\ 1 - \vert x \vert & \vert x \vert < 1 \\ \end{array} \right.$$ (U5)

( $\alpha = -1$)

$$i(x) = \left\{ \begin{array}{ll} (\alpha+2) \vert x\vert^{3} - (\... ...a & 1 \leq \vert x \vert < 2 \\ 0 & 2 \leq \vert x \vert \\ \end{array} \right.$$ (U6)

( $\alpha = -.5 ; \beta = .5$):

$$i(x) = \left\{ \begin{array}{ll} (\alpha-\beta+2) \vert x\vert^{3... ...) & 2 \leq \vert x \vert < 3 \\ 0 & 3 \leq \vert x \vert \\ \end{array} \right.$$ (U7)

(L=6, 8, 16)

$$i(x) = sinc(x)rect({x\over L})$$ (U8)