基于FPGA的FFT算法设计与实现

发布时间：2018-04-14 05:01

本文选题：快速傅里叶变换 + 分裂基　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：数字电子技术和信息技术日新月异，在多媒体应用技术计算机应用图像与语音信号处理，通信服务等众多领域中，都已经广泛地使用到基于数字信号处理的理论与技术快速傅里叶变换(FFT)在很大程度上推动了数字信号处理技术的发展，因为它的运算时间和直接计算离散傅里叶变换(DFT)相比大大减少，更有利于实现数字信号处理的应用，并为数字信号处理技术在实时处理各种信号的应用中提供了优势因此，本文对FFT算法和实现方法的研究对其进一步发展起到了非常重要的理论指导和实践意义经过不断地发展与应用，，可编程逻辑器件FPGA（现场可编程门阵列）正深入地渗透到数字信号处理领域的研究之中，它在不断提高电子设计的规模与集成度的同时，使得电子系统设计方法和设计思想得到了不断地创新本文的研究内容是立足FPGA实现分裂基FFT算法，分裂基FFT算法不仅计算流程图比较简单，而且具有结构良好的特点，更重要的是这种算法在理论上，接近所需乘法次数的最小值本文首先对分裂基FFT算法的理论及原理知识进行了详细的推导，随后与基2FFT和基4FFT算法深入地进行比较说明，并论述了用FPGA实现的方法，使用高效复数乘法器，同时增加了数据溢出的处理本设计以Xilinx公司的Virtex-5系列芯片110T为硬件平台，在ISE14.4编译环境中，用Verilog硬件描述语言对各个功能模块进行功能仿真，最后仿真实现256点的分裂基FFT算法用测试信号对本设计进行测试，并分析仿真结果和MATLAB计算结果的误差，结果表明本文的设计正确
[Abstract]:Digital electronics and information technology are changing with each passing day. In many fields, such as computer application, image and speech signal processing, communication service, etc.Both have been widely used in theory and technology based on digital signal processing, fast Fourier transform (FFT) has promoted the development of digital signal processing technology to a great extent.Compared with the direct calculation of discrete Fourier transform (DFT), its computational time is greatly reduced, which is more advantageous to the application of digital signal processing, and provides an advantage for the digital signal processing technology in the application of real-time processing of various signals.In this paper, the study of FFT algorithm and implementation method plays a very important role in the further development of FFT algorithm and practice.Through the continuous development and application, FPGA (Field Programmable Gate Array) is penetrating deeply into the research of digital signal processing, which improves the scale and integration of electronic design at the same time.As a result, the design methods and design ideas of electronic systems have been innovated continuously.The research content of this paper is to realize split-base FFT algorithm based on FPGA. The split-base FFT algorithm is not only simple to calculate flow chart, but also has the characteristics of good structure.In this paper, the theoretical and theoretical knowledge of split base FFT algorithm is deduced in detail, then compared with base 2FFT and base 4FFT algorithm, and the method of using FPGA is discussed.Using high efficiency complex multiplier and adding data overflow processing, this design takes Virtex-5 series chip 110T of Xilinx Company as hardware platform, in ISE14.4 compiling environment, the function of each function module is simulated by Verilog hardware description language.Finally, a 256-point split-base FFT algorithm is implemented to test the design with test signal, and the error between simulation result and MATLAB calculation result is analyzed. The results show that the design of this paper is correct.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7;TN791

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