ARMA implementation of diffraction operators with inverse-root singularities

TitleARMA implementation of diffraction operators with inverse-root singularities
Publication TypeJournal Article
Year of Publication1990
AuthorsDalton, D. R., and M. J. Yedlin
JournalAntennas and Propagation, IEEE Transactions on
Pagination831 -837
Date Publishedjun.
Keywordsangular 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

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


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