基于FPGA的FFT设计毕业论文.doc

南通大学毕业设计（论文） PAGE I 摘 要 快速傅里叶变换（FFT）是一种为了改进和提高离散傅里叶变换（DFT）运算速度而提出的算法。它是根据已有的DFT的运算特性发展起来的DFT快速算法。快速傅里叶变换的理论在信号处理、数字通信、语音处理和计算机等诸多领域有着广泛的运用。在不同的运用场合，对FFT电路的性能有着不同的要求，但是在很多领域都要求FFT处理器能够具有高速度、高精度和实时性的工作状态。 现场可编程门阵列（FPGA）是由许多独立的可编程逻辑模块组成一种新型可编程器件。FFT运算结构相对比较简单和固定，适合使用FPGA进行硬件实现，并且能兼顾速度及灵活性。本文介绍了一种基于FPGA上实现32点FFT变换的设计方案。整个FFT模块采用基-2时域抽取，顺序输入，逆序输出的方法实现。将采集到的数据通过编写串口程序输入，再运用复数乘法器为核心设计了FFT算法中的基-2蝶形运算单元、溢出控制单元和地址与逻辑控制模块等其它模块，并以这些模块和FPGA内部的双口RAM为基础组成了基-2FFT算法模块，将经过处理的数据由串口程序输出，并且对运算结果使用MATLAB软件对比验证。 关键词：快速傅里叶变换，FPGA，旋转因子，基-2 南通大学毕业设计（论文） 南通大学毕业设计（论文） ABSTRACT Fast Fourier Transform (FFT) is a algorithm in order to improve and enhance the computing speed of the Discrete Fourier Transform (DFT). It is a DFT fast algorithm according to the development of the operational characteristics of the existing DFT. The theory of FFT is widely used in many fields such as signal processing, digital communications, voice processing, and computer. In different applications, the performances of the FFT circuit have different requirements, but in many areas FFT processor is required with high speed, high accuracy and real-time work status. Field Programmable Gate Array (FPGA) is a new type programmable device which is composed by a number of independent programmable logic module. The structure of FFT computation is relatively simple and fixed, suitable for the use of FPGA hardware implementation, and also can take the speed and flexibility into account. This article introduces a 32-point FFT transform design which is based on FPGA. The entire module uses Radix-2 time-domain extraction, the order of input, output reverse method. Input data using the serial interface program and using a complex multiplier as the core design of FFT algorithm in the Radix-2 butterfly unit, overflow control unit and address and logical control module and other modules, and within these modules and FPGA-based dual-port RAM formed the Radix-2 FFT algorithm module, output the processed data from the serial interf