@article {Dalton1990ARMA-implementa,
title = {ARMA implementation of diffraction operators with inverse-root singularities},
journal = {Antennas and Propagation, IEEE Transactions on},
volume = {38},
number = {6},
year = {1990},
month = {jun.},
pages = {831 -837},
abstract = {The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated 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. The authors therefore use a least-squares method to model an equivalent autoregressive moving-average (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 that repaired with 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 direct convolution or 80\% over Fourier convolution, which also has truncation error},
keywords = {angular interpolation, ARMA filter, autoregressive moving-average, coarse spatial sampling, convolutional truncation ghost, CPU time, electromagnetic diffraction, electromagnetic wave diffraction, filtering and prediction theory, infinite tail, inverse problems, inverse-root singularity, least squares approximations, least-squares method, recursive convolution, time-domain analysis, time-domain diffraction operator, truncated difference operator, wavelet},
issn = {0018-926X},
doi = {10.1109/8.55579},
url = {http://dx.doi.org/10.1109/8.55579},
author = {Dalton, D.R. and Yedlin, M.J.}
}