Techniques for Computing the Discrete Fourier Transform Using the Quadratic Residue Fermat Number Systems
Issue No. 11 - November (1986 vol. 35)
T.K. Truong , Jet Propulsion Laboratory
In this correspondence, the complex integer multiplier and adder over the direct sum of two copies of finite field developed in  is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.
VLSI, DFT, error analysis, Fermat number, systolic array
I. ReeD, I. Hsu, T. Truong, J. Chang and D. Pei, "Techniques for Computing the Discrete Fourier Transform Using the Quadratic Residue Fermat Number Systems," in IEEE Transactions on Computers, vol. 35, no. , pp. 1008-1012, 1986.