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This paper uses a method to compute the kernel needed for dispersive scatterer computations numerically. FDDM works by substituting a Z-domain finite difference approximation for the transform variable in the Laplace transformed kernel. The inverse Z-transform of the result is the FDDM kernel. The method described here computes the inverse z-transform directly by integrating in the complex z plane using the trapezoidal rule. This can be done to compute the kernel directly, or to use the FFT to compute the convolution quickly. Finally, the FDDM method is combined with an augmented field approach to stabilize the low frequency behavior of the method.