### IEEE Transactions on Antennas and Propagation abstract

Dalton, D.R. and Yedlin, M.J. (1990) "ARMA Implementation of
Diffraction Operators with Inverse-root Singularities", IEEE Trans.
AP 38, 831-837.
We numerically differentiate the integral of a time-domain diffraction
operator, which has an integrable inverse-root singularity and an infinite
tail, to get a truncated digital form of the operator. This
truncated difference operator effectively simulates the singularity but is
computationally inefficient and produces a convolutional truncation ghost.
We thus use a least-squares method to model an equivalent ARMA filter on
the difference operator. The recursive convolution of the ARMA filter with a
wavelet has no truncation ghost and an error below 1%
of the peak diffraction amplitude. Design and application of the
ARMA filter reduces computer (CPU) time
by 42% over the direct convolution.
A combination of filter design at a coarse spatial
sampling, angular interpolation of filter coefficients to a finer sampling,
and recursive application reduces CPU time by 83% over the direct
convolution or 80% over~the Fourier convolution, which also
has truncation error.