Number Theoretic Transform Modular Residue Processors

G. Eichmann; J. Keybl; R. Mammone

doi:10.1117/12.958294

29 February 1980 Number Theoretic Transform Modular Residue Processors

G. Eichmann, J. Keybl, R. Mammone

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.

Citation Download Citation

G. Eichmann, J. Keybl, and R. Mammone "Number Theoretic Transform Modular Residue Processors", Proc. SPIE 0209, Optical Signal Processing for C3I, (29 February 1980); https://doi.org/10.1117/12.958294

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