1 October 1994 Optical implementation of long data stream convolution
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Long data stream convolution is required by practical signal processing applications. Various algorithms for digital computers offer satisfactory results if the long processing time and large memory space are tolerable. We describe an algorithm suitable to the optoelectronic implementation of the real-time convolution of long data streams (104 to 106 points). Based on the Chinese remainder theorem, an N-point 1-D data sequence (N = r1r2, where r1 and r2 are mutually prime) is permuted to form a r1 x r2 2-D array. The convolution of two N-point 1-D data sequences is then realized by the convolution of their corresponding 2-D arrays. Free space 2-D optical systems can offer the benefit of real-time processing. Due to the huge amount of the required interconnects, optical schemes rather than electronic schemes are preferred to perform the 1-D to 2-D data permutation. We propose to implement a high-speed optoelectronic convolver for handling the long data sequences by using a standard 2-D optical convolver sandwiched between two optoelectronic data permutation devices. A modified cathode ray tube (CRT) and a standard CRT combined with an optical geometric transformer are described as examples of such devices. Various optical implementations of the convolution operation are also described and compared for this application. The entire algorithm was computer simulated for its optical implementation. Other practical problems and the fundamental limits are also discussed.
Yan Zhang, Yan Zhang, Yao Li, Yao Li, H. John Caulfield, H. John Caulfield, } "Optical implementation of long data stream convolution," Optical Engineering 33(10), (1 October 1994). https://doi.org/10.1117/12.179399 . Submission:

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