General source and receiver positions in coarse-grid finite-difference schemes

Coarse grid finite-difference schemes do not allow for general source and r eceiver positions. This problem is here solved with optimized operators wit h general phase-shift properties. These operators are bandlimited represent ations of the Dirac delta function and the derivative of the Dirac delta fu nction. The scheme is tested for a single source and a source array. The re sulting finite-difference solutions are for both cases close to the analyti cal solution.