A sampling theorem is developed to reduce integration error in matrix–vector and linear multiplexing processors that perform discrete versions of continuous linear operations. By simply filtering the operation kernel before sampling, one can perform integration-error-free processing on inputs sampled at their Nyquist rate. Example applications to Laplace and Hilbert transformation are presented.
© 1981 Optical Society of America
Original Manuscript: July 28, 1980
Revised Manuscript: October 17, 1980
Published: January 1, 1981
Robert J. Marks, "Sampling theory for linear integral transforms," Opt. Lett. 6, 7-9 (1981)