Sampling Function

The 1-D sampling function is given by

$$S(x)=\sum_{n=-\infty}^\infty \delta (x-n\Delta x),$$

where $\delta$ is the Dirac Delta Function. The 2-D version is

$$S(u,v) = \sum \delta (u-u_n,v-v_n),$$

which can be weighted to

$$S(u,v) = \sum R_nT_nD_n\delta (u-u_n,v-v_n),$$

where $R_n$ is a reliability weight, $D_n$ is a density weight (Weighting Function), and $T_n$ is a taper.

See also Shah Function, Sinc Function