Title | ARMA implementation of diffraction operators with inverse-root singularities |
Publication Type | Journal Article |
Year of Publication | 1990 |
Authors | Dalton, D. R., and M. J. Yedlin |
Journal | Antennas and Propagation, IEEE Transactions on |
Volume | 38 |
Pagination | 831 -837 |
Date Published | jun. |
ISSN | 0018-926X |
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 |
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 |
URL | http://dx.doi.org/10.1109/8.55579 |
DOI | 10.1109/8.55579 |