大点数FFT的问题研究与分析(论文22000字)
摘 要
对于信号而言。测试结果是执行,FFT设备是好的和浮点节省了大量的资源的折衷。 FPGA适用于实现FFT处理器内部硬件乘法器以及I / O处理单元,为代表),为了避免数据的溢出,MATLAB仿真FFT算法证明了该方法的正确性。与此同时信号率信噪比的增加,和复杂性,同时相对的ASIC中含有一个程序存储器和含有大量的成本低,同时提高了处理器的时钟频率的数据处理速度的方法,使用查表的存取方法,以确保准确性的操作,从而使得设备的成本升高。
【关键词】:大点数FTT;傅里叶变换;信号频域空间
ABTRACT
For signals, you want to transform from the time domain to the frequency domain, and a necessary condition for the fast Fourier transform (FFT) is the basic operation of the digital spectrum analysis in the frequency domain implementation. The real-time software and the FFT operation based on a DSP application specific integrated circuit (ASIC) and programmable logic devices (in the field programmable gate array (FPGA), as represented), generally using conventional high-speed processing is realized, and the appearance is difficult meet. At the same time the rate of increase in the signal to noise ratio, the number of transition points of the increase, the area of ASIC chip operating unit is expanding rapidly, so that the cost of the device increases. FPGA FFT processor suitable for implementing internal hardware multiplier and I / O processing unit, while the opposite ASIC contains a program memory and contains a lot of low cost, easy to debug and competitiveness and can be reprogrammed.
This article focuses on the study for the design and implementation of a large number of points of the FFT processor.
(1) FFT is the time decimation algorithm (DIT) algorithms and high-speed real-time systems 5-4, the core unit and piping butterfly algorithm processor pipeline and improved design saves about 75% of the hardware area in order to achieve this requirement also increases the speed of zoom operation. ROM memory, and a rotation factor, saving time and effort by using Table access mode, designed to control the dual-port RAM data storage
(2) FFT is simple and fast.
(3) the use of a block floating-point data structure, in order to prevent an overflow of data, FFT and floating-saving device is a good trade off a lot of resources.
(4) Finally, verify hardware implementation of FFT algorithm, MATLAB simulation FFT algorithm proves the correctness of the method. The test results are performed to ensure the accuracy of the operation, and complexity, while improving the processor's clock speed data processing speed of the method, and that it is possible to achieve the intended purpose.
【key words】:Great points FTT; Fourier transform; signal in the frequency domain space
目 录
摘 要 II
ABTRACT III
目 录 V
第一章 绪论 1
第一节 研究背景 1
第二节 国内外的研究现状 2
第二章 大点数FFT变换的理论知识 4
第一节 傅里叶变换理论知识 4
第二节 DFT的发展 5
第三节 高效的DFT的计算——FFT算法 6
第四节 FFT 算法的规律 7
第三章 大点数FFT算法的概念和应用 9
第一节 频域抽取的基2算法 9
(一)正变换的计算 9
(二) 逆变换的计算 12
第二节 时域抽取的基2算法 13
第三节 一维FFT算法的应用 15
(一) 利用FFT计算连续时间信号的傅里叶变换 15
(二) 利用FFT计算离散信号的线性卷积 19
(三) 利用FFT进行离散信号压缩 22
(四) 利用FFT对离散信号进行滤波 26
(五) 利用FFT提取离散信号中的最强正弦分量 30
第四节 二维DFT的快速变换算法及应用简介 35
(一) 二维FFT变换及其算法介绍 35
(二) 二维FFT变换算法的应用 36
第四章 大点数FFT算法的改进及其实现 37
第一节 大点数FFT算法的改进 37
第二节 关于FFT的计算效率的研究 39
第三节 FFT中窗函数的研究 42
第五章 总结与展望 44
参考文献 45