2009 Volume 6 Issue 14 Pages 1019-1024
The existing cyclic convolution based on Fermat number transform(FNT) can't produce the same results as the conventional one based on fast Fourier transform (FFT) due to the impact of modular operation in many cases. To overcome the problem, this paper proposes a novel data-recovery algorithm (DRA) for the cyclic convolution based on FNT with transform kernel 2 or its integer power in the ordinary binary number system. Then an efficient data-recovery circuit (DRC) is designed to implement the algorithm in the diminished-1 number systems, involving parallel-prefix carry computation units. The DRA and the DRC can eliminate the impact of modular operation and make the cyclic convolution based on FNT produce the correct resulting sequences. Synthesis results show that delay and area of the n-bit DRC are both less than the ones of an n-bit parallel-prefix adder (PPA).