DFT的循环卷积算法推导及其FPGA实现

Algorithm Design and FPGA Realization of Convolution DFT

首先提出了数论中的原根成对存在定理 ,并进行了详细的数学证明。然后根据原根可使数环重新排序的性质 ,利用一对原根对 DFT运算的输入和输出序列重新排序 ,推导出 DFT的循环卷积算法 ,进一步给出了此算法的结构图。最后给出了用 VHDL 语言实现该算法的完整程序、仿真结果及分析 ,并总结了用 FPGA实现

In this paper, a theorem of primary root exists as a couple in the Number Theory was suggested, and detailed mathematic proof was given. Based on the character of primitive root can reorder the number ring and using the two primary root to reorder the input and output sequences of the DFT computation, a algorithm of DFT cyclic convolution was deducted and further structure diagram was given. At the end, a complete program written in VHDL language for this algorithm, the simulating result and analysis are given. The importance of achieving the DFT computation by using FPGA was summarized.