基于ModelSim的FFT算法的设计

理工大学学士学位论文I摘要快速傅立叶变换(FFT)作为时域和频域转换的基本运算，是数字谱分析的必要前提。传统的FFT使用软件或DSP实现，高速处理时实时性较难满足，因此专用集成电路(ASIC)和可编程逻辑器件(以现场可编程门阵列FPGA为代表)应运而生。速度上ASIC更占优势，但是随着点数的增加，芯片面积将迅速扩大，也就意味着成本的提高。而FPGA内部含有硬件乘法器，大量的存储单元和可编程I/O，十分适合于FFT处理器的实现，而且相对ASIC，成本低廉，可以反复编程，便于调试，也更具市场竞争力。本文应用Verilog语言完成32点基-2复数的FFT处理系统设计，包括蝶形运算单元设计、存储单元设计、块浮点单元设计、地址产生单元设计、功能切换单元设计以及时序控制单元的设计工作。以选取的FPGA器件库为基础，使用modelsim软件进行仿真，并对结果进行分析。关键词：快速傅立叶变换；Verilog；单元设计；modelsim仿真理工大学学士学位论文IIAbstractFastFourierTransformisanecessarypreconditionofdigitalspectralanalysisasthebasiccomputingbetweenthetimedomainandfrequencydomain.ThetraditionalFFTusessoftwareorDSPtorealize,whichisdifficulttomeetreal-timeinhighspeedprocessing.Applicationspecificintegratedcircuit(ASIC)andprogrammablelogicdevice(representedbyfieldprogrammablegatearray,FPGA)arisesatthehistoricmoment.ASIChastheadvantageinthespeed,butthechipareawillexpandrapidlywiththeprocessingpointsincreasing,whichmeanstheimprovementofcosts.WhileFPGAcontainshardwaremultipliers,massivememorycellsandprogrammableI/O,soitisverysuitableforimplementationofFFTprocessor.Therefore,FPGAislow-cost,easytodebugandcanberepeatedlyprogrammed.Ithasmoremarketcompetitiveness.UseVeriloglanguagecompleted32points2complexFFTprocessingsystemdesign,Includingbutterflycomputingunitdesign,storageunitdesign,blockfloating-pointunitdesign,theaddressgenerationunitdesign,thefunctionswitchunitdesignandtimingcontrolunitdesignwork.OnthebasisoftheselectedlibraryastheFPGAdevice,usethemodelsimsimulationsoftware,andanalyzetheresults.KeyWords:FFT;Verilog;Unitdesign;modelsimsimulation理工大学学士学位论文III目录1绪论...................................................................11.1课题的背景及意义......................................................................................................11.2FFT的国内外发展研究现状.......................................................................................21.2.1通用数字信号处理芯片....................................................................................21.2.2专用集成电路芯片ASIC..................................................................................31.2.3可编程逻辑器件................................................................................................31.3篇章结构......................................................................................................................52离散福利叶变换的快速算法的基本理论.....................................62.1基-2FFT算法...............................................................................................................62.2定点数的相关概念....................................................................................................152.2.1定点数的定义.................................................................................................152.2.2定点数加减法的溢出及检测方法.................................................................152.3定点数的定标............................................................................................................162.4有限字长效应............................................................................................................162.5块浮点数....................................................................................................................173FFT的算法设计.........................................................183.1FFT处理器的实现框图.............................................................................................183.2蝶形运算单元的设计................................................................................................183.3流水线结构................................................................................................................253.4存储单元的设计........................................................................................................263.4.1FFT数据存取规律分析..................................................................................263.4.2双口RAM及其地址发生器的设计..............................................................273.4.3ROM及其地址发生器的设计.......................................................................303.5浮点单元的设计........................................................................................................333.6时序控制单元的设计................................................................................................384基于verilog语言的FFT的设计与仿真.....................................404.1ModelSim介绍...........................................................................................................404.2ModelSim仿真...........................................................................................................404.2.1建立工程..........................................................................................................41理工大学学士学位论文IV4.2.2加载文件..........................................................................................................414.2.3开始仿真..........................................................................................................424.3结果分析....................................................................................................................44结论...............................................