29 February 1980 Number Theoretic Transform Modular Residue Processors
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Proceedings Volume 0209, Optical Signal Processing for C3I; (1980) https://doi.org/10.1117/12.958294
Event: Optical Signal Processing for C3l, 1979, Boston, United States
Abstract
Finite digital convolution (FDC) appears in the implementation of finite impulse response digital filtering, in auto-aid cross-correlation, polynominal multiplication and the multiplication of very large numbers. While there are several methods to implement FDC, when the lengths of the sequences to be convolved is a highly composite number, the discrete fast Fourier transform (FFT) approach is used. This approach requires generating, storing and truncating a large number of complex exponentials. Recent interest has centered on finding real basis numbers that preserve the properties of the FFT. By working in a finite field of integers with arithmetic modulo an integer M, a large class of new transforms, called number theoretic transforms, can be generated. These transforms are useful in applications where integer arithmetic is already being considered, such as spread-spectrum encoding, digital error-correction and data encryption, or where the data is digitally encoded in a finite number of bits. In this paper, residue arithmetic based number theoretic transforms will be considered.
© (1980) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
G. Eichmann, G. Eichmann, J. Keybl, J. Keybl, R. Mammone, R. Mammone, } "Number Theoretic Transform Modular Residue Processors", Proc. SPIE 0209, Optical Signal Processing for C3I, (29 February 1980); doi: 10.1117/12.958294; https://doi.org/10.1117/12.958294
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