Abstract

Radar, sonar, and communications often require that long data streams containing, perhaps, more than one million data points be convolved or correlated. Conventional digital electronic computers with serial processing hardwares are not capable of handling such operations in real time. Although various mathematical models exist that decompose long data streams into a set of shorter streams to be processed in parallel for convolution/correlation, the actual digital electronic hardware to implement these algorithms may be too complicated. In this paper, a number-theoretic transform algorithm that is suitable for an optical implementation is studied for performing hybrid convolution/correlation of long data streams. The 1-D input and reference data streams are permuted to form arrays of shorter data sequences in 2-D formats, which are then optically convolved/correlated via a standard Fourier optics method. The 2-D convolution/correlation obtained result is finally shuffled back to obtain the 1-D convolution result.

© 1991 Optical Society of America