Expansion in Exponential Sums with Application to Discrete Complex Image Theory

Expansion of functions in terms of exponential sums is a technique that has been used in the past for applications in applied mathematics such as number theory. However, the technique also has interesting applications in the field of engineering. In this paper we present a novel approach to deriving an expansion of a function as an exponential sum and show how this expansion can be applied to the Sommerfeld Integral to give a novel Discrete Complex Image representation.