最小SD数表現を用いた剰余演算とFIRフィルタ回路への応用

摘要

Residue arithmetic based on a radix-two signed-digit (SD) number system was proposed. Compared to the design of conventional residue arithmetic circuit which is using binary number system, the speed of operation was significantly improved, but the area of circuit increased accordingly. This paper considers the problem about on residue arithmetic how to convert a number which is in SD representation to its minimal signed-digit (MSD) representation. Our experimental results show that maximally the speed and the hardware complexity of residue arithmetic circuit are reduced by 64.5% and 88.7% respectively. We also discuss the possibility of implementing residue arithmetic using MSD to FIR filter.%2進signed-digit（SD）数を用いた剰余演算が提案されている.従来の2進数を用いた剰余演算に比べて，演算速度が著しく改善されたが，回路面積が相対的に増大した.本論文では，剰余数系でSD数を最小SD数（Minimal Signed-Digit）表現に変換する方法を提案し，実験結果により剰余演算回路の演算量とハードウェア複雑さがそれぞれ最大64.5％と88，7％減少することを示す.また，最小SD数表現を用いた剰余演算を定係数FIRフィルタ回路に導入する応用の可能性を論ずる.