计算2~m×2~m点二维离散Fourier变换的新算法

本文提出了一种计算2~m×2~m点二维离散Fourier变换的新算法。此法与一维FFT逐行逐列计算二维DFT的算法相比,优点是减少25～71％的复数乘法运算。文中还讨论了产生旋转因子和二维反序重排的快速算法。     

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.     

二维Tchebichef矩正反变换的快速算法

本文提出了一种二维Tchebichef矩正反变换的快速算法。在正变换中,使用Chebichef递推公式推导了一维Tchebichef矩正变换的快速算法,并将其推广至二维Tchebichef矩正变换的快速计算。在反变换中,使用Clenshaw递推公式我们推导了一维Tchebichef矩反变换的快速算法,并将其推广至二维Tchebichef正交矩反变换的计算。与以迭代方式计算Tchebichef多项式进而计算二维Tchebichef矩正反变换的方法相比,本文算法有效地减少了算术运算的次数,提高了计算速度。实验结果表明了该方法的有效性。     

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.     

基于Zak变换和FRFT的风廓线雷达间歇杂波抑制

间歇杂波严重干扰了风廓线雷达大气湍流回波信号的识别和频谱估计。为了抑制该类杂波,提出了基于Zak变换和分数阶Fourier变换（FRFT）的杂波抑制方法,该方法利用Zak变换估计杂波调频率参数,然后根据杂波在分数阶Fourier域的能量聚集特性滤除杂波。与经典FFT信号处理方法相比,杂波抑制效果明显;与FRFT扫描法相比,将杂波检测二维搜索问题简化为一维搜索问题,简化了计算。并通过信杂比改善因子对该算法性能进行分析,杂波抑制后信杂比有较大提高。理论和计算机仿真证明了该方法的有效性。     

基于频域遮隔及分数阶相关的反辐射导弹检测技术

该文提出一种基于频域遮隔及分数阶相关来检测反辐射导弹(ARM)的新方法。该方法利用雷达回波的频域(Fourier变换)数据,根据尖锋作遮隔处理后,直接运用基于分数阶Fourier变换(FrFT)和Fourier逆变换的分数阶相关方法,通过一维搜索来检测ARM。由于该方法利用了现有的Fourier数据,且分数阶Fourier变换可以通过Fourier变换实现,无需多通道相位补偿和二维搜索,故计算量小。仿真结果表明,该方法能够在ARM信噪比低达#61485;10dB,ARM与载机回波功率比为#61485;27dB的情况下,准确地检测出ARM,从而实现ARM发射的早期告警。     

PAL信号的数字解调

本文讨论了基于NTSC和PAL彩色全电视信号的二维沃尔什序谱分析的彩色解调器。指出在亮度信号和色度信号分离性能上,二维解调比一维解调好。二维解调有二维沃尔什变换和二维滤波二种方法。利用一维沃尔什函数和二维沃尔什函数的关系,可以用一维列率滤波器来实现NTSC及PAL信号的二维亮色序谱的分离。     

基于MATLAB engine的自动控制理论仿真实验设计

介绍了一种通过采用MATLAB engine函数进行数据传输的MATLAB与VC＋＋联合编程的方法,并给出在“自动控制理论”仿真实验中的应用。这种方法用VC＋＋设计前台用户界面,将MATLAB作为后台的计算与绘图引擎。因此无需学生掌握MATLAB语言的编程方法,就能达到仿真实验目的,掌握控制理论的关键知识点。     

用计算全息制作二维Haar小波变换滤波器的研究

提出了用计算全息制作三类Haar子波滤波器的方法。将一维Haar子波函数组合,将得到三种类型的二维Haar子波函数,利用这三类二维Haar子波可以分别对图像进行角、水平边和垂直边的提取。采用罗曼Ⅲ型迂回位相编码法对三类Haar子波函数进行编码,绘出计算全息图。为了提高全息图的质量,采用显示器分屏抓图的办法,将全息图分割输出。在4f系统中实现对二维图像的三类Haar子波变换,给出了提取二值图像特征的模拟结果。     

图像小波变换VC程序实现

目前,小波理论应用已成为物理、数学和计算机等学科研究的热点,其中小波理论最成功的应用就是在图像处理中。在小波变换中,人们一般多运用MATLAB作为工具来进行图像处理的研究实现,但是在调用MATLAB小波工具箱的相关函数对小波进行构造时,往往忽略了对底层函数的理解,这对小波的进一步研究带来了不便。本设计重点阐述了二维离散小波变换的Mallat算法实现原理,并运用C＋＋编程实现,这改进了在MATLAB中不足之处,并且在MFC基础上进行了编程,得到一个可视化窗口,更加清晰地体现小波变换算法的核心。     

A convergence acceleration procedure for computing slowlyconverging series

The application of shaped &thetas;-algorithm to the partial sums of a slowly converging series is shown to accelerate its convergence. The algorithm is applied to accelerate the convergence of a series representing the free-space periodic Green's functions involving the zeroth-order Hankel function of the second kind, and its associated Fourier transform. Numerical results indicate that the algorithm converges faster than Shanks' transform. It is also able to sum the series to machine precision in about 20 terms. A relative error measure is shown as a function of the number of terms of various combinations of source and observation points. The relative savings in computation time is also provided to show the benefit of using the algorithm     

Efficient calculation of lattice sums for free-space periodicGreen's function

An efficient method to calculate the lattice sums is presented for a one-dimensional (1-D) periodic array of line sources. The method is based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function. The lattice sums of arbitrary high order are then expressed by an integral of elementary functions, which is easily computed using a simple scheme of numerical integration. The calculated lattice sums are used to evaluate the free-space periodic Green's function. The numerical results show that the proposed method provides a highly accurate evaluation of the Green's function with far less computation time, even when the observation point is located near the plane of the array     

任意平面分层介质中正演计算的快速方法

在非均匀介质电磁散射、逆散射等领域中，正演计算速度直接影响着反演计算效率。快速高精度的正演计算方法有利于反演效率的改善。对于任意平面分层介质情形，传统高效的数值模式匹配法的正演计算效率并不很高。本文通过首先推得每一从向分层中场量的汉克尔变换表达，再用快速傅里叶变换来完成汉克尔变换计算，从而得到更高效的计算方法。它避免了数值本征模式的求解，特别适用于处理平面分层介质中纵向分层较多的情形。对于其它非均     

A Reconstruction Algorithm for Photoacoustic Imaging Based on the Nonuniform FFT

Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.      

Fast Hankel transform by fast sine and cosine transforms: theMellin connection

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure that does not require exponential sampling is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into a sine, a cosine, and an inversion transform, which can be implemented by means of fast sine and cosine transforms     

On the use of ρ-algorithm in series acceleration

The ρ-algorithm, a nonlinear transformation, is shown to be applicable to monotonic series. The results of applying the algorithm to a series involving the zeroth-order Hankel function of the second kind and its associated Fourier transform are given. It is shown that the algorithm performs better than the ϵ-algorithm derived from Shanks' transform (1955). Numerical results include a relative error measure versus number of terms taken in the series     

线性调频信号时/频差快速联合估计方法

提出了一种线性调频(Chirp)信号时/频差估计算法。首先估计Chirp信号互模糊函数中脊线的位置,再通过频率补偿使脊线通过原点,进而通过搜索信号在分数阶傅里叶变换域上的相关峰来代替沿脊线搜索模糊函数峰值的过程,最终获得时/频差的估计。该算法由于采用一维搜索,并且可用快速傅里叶变换实现,因此所需运算量显著降低。对于多分量Chirp信号,根据脊线位置的不同,算法能够分别估计出各分量信号的时/频差。仿真实验表明,该算法能够精确估计Chirp信号的时/频差,并且随着信噪比的提高,时/频差估计值的均方根误差逐渐接近克拉美罗下界。      

A procedure for calculating the atmospheric mutual coherencefunction via the statistical Fourier-optical method

An algorithm is presented for computing the atmospheric mutual coherence function at optical and millimeter wavelengths from flux measurements taken at the focal plane of a reflector antenna. The procedure consists of first computing the inverse Abel transform of the flux, taking the Fourier transform of the result, and then dividing by the aperture pupil function. It is shown that when the flux measurements contain additive noise, the Abel inversion is an ill-posed problem. Therefore, calculation of the inverse Abel transform is accomplished by a Kalman filtering algorithm. Results of the mutual coherence function estimator are given for simulated flux measurements     

应用Winograd傅氏变换算法计算傅里叶光谱

讨论了Ｗｉｎｏｇｒａｄ傅里叶变换算法的优点,通过计算表明,将其应用于傅里叶变换光谱的具体算法时,与计算的具体过程相结合,可显著地提高光谱的计算效率     

A concurrent implementation of the prime factor algorithm onhypercube

The prime factor algorithm (PFA) is an efficient discrete Fourier transform (DFT) computation algorithm in which a one-dimensional DFT is tuned into a multidimensional DFT, consisting of a few short DFTs whose lengths are mutually prime, and then an efficient algorithm is used for the short DFTs. The PFA was implemented on a hypercube using CrOS III communication routines, taking 120 ms to compute the DFT of 5040 complex points using 32 nodes of the Caltech-JPL MARK III Hypercube. It took 105 ms to do a DFT of 4096 complex points using the Cooley-Tukey algorithm with the same hardware configuration. The performance of hypercubes MARK III, NCUBE, and iPSC and the relative importance of communication and calculation are analyzed. With the current communication speed the Cooley-Tukey algorithm performs fast on a massively concurrent processor and the PFA is advantageous when the number of processors is less than 64 or so. The experience with using the PFA also serves as a useful guide to a multidimensional fast Fourier transform implementation using any algorithm