离散傅里叶变换的算术傅里叶变换算法

离散傅里叶变换(DFT)在数字信号处理等许多领域中起着重要作用.本文采用一种新的傅里叶分析技术—算术傅里叶变换(AFT)来计算DFT.这种算法的乘法计算量仅为O(N);算法的计算过程简单,公式一致,克服了任意长度DFT传统快速算法(FFT)程序复杂、子进程多等缺点;算法易于并行,尤其适合VLSI设计;对于含较大素因子,特别是素数长度的DFT,其速度比传统的FFT方法快;算法为任意长度DFT的快速计算开辟了新的思路和途径.     

一维长序DFT的协处理阵列结构设计与实现

文章针对一维长序DFT计算问题，分析其计算结构以及算法的并行性，提出一种阵列协处理结构．并分析这种协处理机结构上DFT计算的组织及具体实施算法步骤和方法，并对这种协处理阵列结构上运行的DFT进行复杂性分析。这对计算DFT专用集成协处理结构芯片开发，提高专用嵌套系统性能非常实用。     

基于DFT的OFDM系统信道估计改进算法

基于DFT的信道估计算法计算复杂度比MMSE算法低,性能比LS算法好.但是传统的基于DFT的信道估计只消除了信道冲击响应估计中循环前缀长度之外的噪声,循环前缀长度内的噪声并没有得到抑制,因此算法性能还有提高的空间.本文提出了一种改进的基于DFT的信道估计算法.算法首先估计出噪声方差,然后利用噪声方差设定一个门限,通过此门限对循环前缀内的信道时域冲击响应值进行阈值,进一步消除噪声的干扰.仿真证明,本文的改进信道估计算法性能优于原算法.     

多维DFT的多维多项式变换与离散W变换算法

本文首先通过引进一种序列的重排技术将m(m2) 维离散Fourier变换 (m-D DFT)转化为一系列的一维广义离散Fourier变换(GDFT)的多重和.然后引入一维离散W变换(DWT)以及多维多项式变换(MD-PT)计算该多重和以减少冗余的算术运算,从而得到了高效的多维DFT算法,该算法与常用的行-列DFT算法相比,乘法仅约为行-列法的1/2m,而加法仅约为行-列法的(2m+1)/4m.对于2维DFT的计算,本文方法同单纯的多项式变换方法相比,乘法与加法分别减少50%与40%左右.另外,本文算法计算结构简单,易于编程实现,通过数值实验验证了本文算法的高效性.     

滑动DFT算法在功率谱估计中的应用

基于滑动DFT算法推导出一种改进的周期图功率谱估计方法,并在软件系统界面中应用。根据传统的功率谱估计方法和滑动DFT算法推导出改进的功率谱估计算法,通过滑动D丌算法计算出DFY值,计算DFT时通过加窗减少了频谱泄漏．然后通过周期图法计算出最终的功率谱值,在Matlab中绘制出功率谱进行验证,用C＋＋语言对该算法进行实现...     

一种改进的二维离散极坐标Fourier变换快速算法

在雷达天线、图象配准、图象检索等领域内常常需要用极坐标表示二维数字信号的离散Fourier变换(DFT).与笛卡尔坐标系下的二维DFT不同,二维离散极坐标Fourier变换(DPFT)不具有行列可分性,直接计算非常耗时.本文提出一种改进的DPFT的快速算法.该算法针对二维阵列实信号,算法全部过程可用一维运算实现,大大降低了计算复杂度并且适用于实时处理.实验中与直接运算方法相比较,显示了该算法的良好性能.     

DFT和卷积计算中的一维到多维映射

本文利用有限交换环的基本概念和性质讨论了DFT和卷积计算中的一维化多维问题。文中论述了DFT一维化多维同Levy-Walsh变换的关系,论证了利用多维技术计算一维DFT和循环卷积时序号变换的充要条件,并给出了一种序号重排快速算法。     

一种频率无关的正弦信号相量计算方法

为寻求一种频率无关的实时相量计算方法,通过分析传统算法,提出一种可变数据窗正弦相量插值计算方法。该算法通过等间隔采样获得信号一个周期左右的样本数据,采样数据计算出信号的基波频率并确定信号的一个基频周期所需的最大采样点数N,计算信号N点DFT和N+1点DFT,再利用两次DFT计算结果进行线性插值得到信号真实频点上各次谐波的实部和虚部,计算出信号各次谐波的幅值和瞬时相位。仿真分析和实际测量表明,该算法的计算精度和实时性较高,能够满足频率随机变化的应用要求。     

基于SC-FDMA系统的噪声估计算法研究

为了提高单载波频分多址接入(SC-FDMA)系统的性能,一种简单且有效的基于探测参考信号(SRS)的噪声估计算法是必要的.针对传统基于离散傅里叶变换(DFT)算法的缺陷,提出了一种改进的基于DFT的算法.另外,在该改进的基于DFT的算法的基础上,又通过增加汉宁窗进行修正,减小了高信噪比下信号能量的泄露.仿真结果表明,在低信噪比下,改进的基于DFT的算法的性能相比传统的算法性能上有4 dB的改善.但是,在高信噪比下,改进的基于DFT的算法的性能逐渐变差,而通过添加汉宁窗却能修正这一缺陷,使其性能得到至少4 dB的改善.     

DCT,DHT与DFT脉动阵列实现

本文提出一种新型计算离散正交变换如DCT、DHT(DWT)和DFT的脉动阵列实现.脉动算法是基于Vetterli-Nussbaumer提出的FFCT和三角函数递归公式.文中绐出了两种基于特殊蝶形运算的处理单元和两种计算DCT,DHT(DWT)和DFT的脉动阵列实现.利用两种不同的DCT脉动阵列的特点,文中也给出了二维DCT脉动阵列实现,所有运算都在实数域中进行.由于这些计算具有高度的简便性、规则性、灵活性和一致性,它们的超大规模集成实现将是有效的.     

Switched-capacitor DFT and IDFT circuit

The switched-capacitor realization of the discrete Fourier transform (DFT) is treated in this paper as well as the inverse discrete Fourier transform (1DFT). The output of the DFT has a sinusoidal waveform including the amplitude and phase information of the required spectra. These spectra are given simultaneously and almost in real time. The output of the 1DFT is given merely by adding DFT outputs. Furthermore, the circuit configuration of this system-from input to DFT, from DFT to 1DFT, and from 1DFT to output-is a very simple configuration constructed by a non-recursive filter circuit.     

The sliding DFT

The sliding DFT process for spectrum analysis was presented and shown to be more efficient than the popular Goertzel (1958) algorithm for sample-by-sample DFT bin computations. The sliding DFT provides computational advantages over the traditional DFT or FFT for many applications requiring successive output calculations, especially when only a subset of the DFT output bins are required. Methods for output stabilization as well as time-domain data windowing by means of frequency-domain convolution were also discussed. A modified sliding DFT algorithm, called the sliding Goertzel DFT, was proposed to further reduce the computational workload. We start our sliding DFT discussion by providing a review of the Goertzel algorithm and use its behavior as a yardstick to evaluate the performance of the sliding DFT technique. We examine stability issues regarding the sliding DFT implementation as well as review the process of frequency-domain convolution to accomplish time-domain windowing. Finally, a modified sliding DFT structure is proposed that provides improved computational efficiency.     

Low-complexity FFT structures for OFDM transceivers

Orthogonal frequency-division multiplexing is a multiple-access technique with modulation and demodulation implemented by an inverse discrete Fourier transform (DFT) and a DFT, respectively. In a downlink (uplink) environment, an individual receiver (transmitter) may only use a small number of subchannels at any given time, in which case it does not make sense to require full DFT demodulation (inverse DFT modulation). Several existing low-complexity techniques for computing a partial DFT or inverse DFT with power-of-two size are examined. Low-complexity fast Fourier transform structures for full, few input, and few output nonpower-of-two transforms are derived.     

A simple interpolation technique for the DFT for joint system parameters estimation in burst MPSK transmissions

In this paper, we propose a simple frequency-domain interpolation technique for the discrete Fourier transform (DFT). This interpolation technique can significantly improve the frequency and phase resolution capabilities of the DFT without increasing the size of the DFT (the number of points used for the DFT). This new technique employs a dividing point in the amplitude and phase spectra. Suitable areas of application include joint estimation of fine frequency and phase offsets in burst-mode digital transmission.     

Low-Cost Fast VLSI Algorithm for Discrete Fourier Transform

A primeN-length discrete Fourier transform (DFT) can be reformulated into a (N-1)-length complex cyclic convolution and then implemented by systolic array or distributed arithmetic. In this paper, a recently proposed hardware efficient fast cyclic convolution algorithm is combined with the symmetry properties of DFT to get a new hardware efficient fast algorithm for small-length DFT, and then WFTA is used to control the increase of the hardware cost when the transform length Nis large. Compared with previously proposed low-cost DFT and FFT algorithms with computation complexity of O(logN), the new algorithm can save 30% to 50% multipliers on average and improve the average processing speed by a factor of 2, when DFT length Nvaries from 20 to 2040. Compared with previous prime-length DFT design, the proposed design can save large amount of hardware cost with the same processing speed when the transform length is long. Furthermore, the proposed design has much more choices for different applicable DFT transform lengths and the processing speed can be flexible and balanced with the hardware cost     

Computation of an odd-length DCT from a real-valued DFT of the samelength

The discrete cosine transform (DCT) is often computed from a discrete Fourier transform (DFT) of twice or four times the DCT length. DCT algorithms based on identical-length DFT algorithms generally require additional arithmetic operations to shift the phase of the DCT coefficients. It is shown that a DCT of odd length can be computed by an identical-length DFT algorithm, by simply permuting the input and output sequences. Using this relation, odd-length DCT modules for a prime factor DCT are derived from corresponding DFT modules. The multiplicative complexity of the DCT is then derived in terms of DFT complexities     

基于FPGA的24点离散傅里叶变换结构设计

基于Good—Thomas映射算法和ISE快速傅里叶变换IP核,设计了一种易于FPGA实现的24点离散傅里叶变换,所设计的24点DFF模块采用流水线结构,主要由3个8点FFT模块和1个3点DFT模块级联而成。并且两级运算之间不需要旋转因子,整个DFF模块仅仅需要14个实数乘法器,布局布线后仿真工作时钟频率可达200MHz。首先根据Good—Thomas算法将并行的24路输入信号分成3组,每组8路信号,并进行并／串转换,得到3路串行信号;其次。将3路串行信号分别输入至3个FFrIP核模块进行8点FFT运算;然后,将上述3个FFrIP核模块同一时刻输出的3路信号进行3点DFF变换;最后,将得到的3路并行输出信号分别进行串／并转换,得到24路DFF输出信号。此外,设计的24点DFT结构还具有很好的扩展性,通过修改FFTIP核变换点数参数便可实现长度N=3×2^N点DFT。     

弹性分组环专用集成电路的可测性设计

根据弹性分组环专用集成电路的具体情况,提出了相应的可测性设计(Design for Test-ability,DFT)方案,综合运用了三种DFT技术:扫描链、边界扫描测试和存储器内建自测试。介绍了三种技术的选取理由和原理,对其具体实现过程和结果进行了详细分析。DFT电路的实现大大降低了专用集成电路的测试难度,提高了故障覆盖率。     

从DFT导出过程和频谱分析谈DFT教学

信号处理中离散傅里叶变换DFT是一个重要的计算手段,可以完成很多计算,包括对连续时间信号的频谱估计。这在教学中是一个重点和难点。本文构建了由连续时间傅里叶变换CTFT和离散时间傅里叶变换DTFT导出DFT的过程,通过一系列操作和推导,以此理解DFT和DTFT以及离散时间傅里叶级数DTFS的密切联系,并深刻体会利用DFT做频谱分析的特点和考虑。