基于FFT的矩形阵波束形成算法

为提高矩形阵的波束形成算法的效率,在波束形成中引入了快速傅立叶变化.基于快速傅立叶变换,将阵所接收的数据从时域变换到频域,通过对相位进行均分,使数据在空间域上进行排序重组,再次利用快速傅立叶变换从空间域转化到波数域上,经过相位修正形成波束图.仿真实验表明,随着阵元数增大,采用快速傅立叶变换能有效降低运算量,提高运算速度,降低对硬件的要求,易于工程实现.     

基于TMS320C6201的离散分数阶傅立叶变换快速算法详细实现

各种离散分数阶傅立叶变换DFRFT(Discrete Fractional Fourier Transform)算法的发展促进了分数阶傅立叶变换FRFT(Fractional Fourier Transform)在数字信号处理领域的应用。本文首先介绍了FRFT的定义和特性,并给出了几种DFRFT计算方法的比较。在对Ozaktas提出的DFRFT快速算法理论分析基础上,本文给出了基于TMS320C6201定点数字信号处理器DSP(Digital Signal Processor)的快速算法详细实现。该详细充分利用FFT计算和数学处理来有效降低算法的运算量。     

基于FFT的三维CAD模型形状描述

针对三维CAD模型,以快速傅立叶变换为基础,建立了一种CAD模型几何形状描述方法.首先,在对模型几何面进行统一表示的基础上,根据模型边界表示中的面片邻接信息,采用完全图旅行商回路算法建立模型的面片序列,并由参考模型保证面片序列的一致性;然后,根据面片序列将模型几何信息转换为5个一维离散信号,并对信号进行采样和幅度缩放,通过快速傅立叶变换(Fast Fourier Transform,FFT)将信号转换到频域,以频域振幅作为三维CAD模型几何形状的描述.如果忽略面片序列引起的偏差,该方法描述模型几何形状的能力与FFT描述离散信号的能力类似.通过实例阐述了描述方法的直观可解释性.     

矢量水听器阵波束域MUSIC算法研究

矢量水听器可同时拾取声压和振速信息,成阵后水听器间的相移信息量增大。基于矢量水听器阵的波束形成性能明显由于同条件下的声压水听器阵,但其空间分辨力依然受阵列物理空间的限制。已经有人研究了矢量水听器阵的高分辨谱估计方法（MUSIC算法）,但属于对阵元域信号进行的直接处理,运算量较大。提出一种基于矢量水听器阵的波束域MUSIC算法（BMUSIC）。该算法首先将矢量水听器阵元的空间数据转换到波束空间,然后对转换后的数据再运用MUSIC算法。不但实现了降维处理,减小了运算量,而且可进一步抑制扫描扇面外的噪声。对BMUSIC算法进行了仿真并与常规MUSIC算法进行了比较。结果表明,该方法可得到与阵元域MUSIC算法相当的方位分辨力。     

基于遗传算法的宽带目标波束空间DOA估计

提出一种基于遗传算法的宽带目标到达方位(DOA)估计新方法,该方法首先通过傅立叶变换方法设计频域恒定束宽转换矩阵,并使用该矩阵将阵元空间的数据转换到波束空间,同时,利用宽带波束空间遗传算法进行DOA估计。计算机仿真表明:在低信噪比条件下该算法相比于CSS类子空间算法、CSS类最大似然算法和阵元空间遗传算法有更高的分辨概率,更小的均方误差。     

基于均匀圆阵的LFM信号DOA估计

针对为解决对雷达和通信中的线性调频信号源(LFM)定位的难题,为提高定位精度,提出了一种基于均匀圆阵的测向定位方法.方法通过分数傅立叶变换(FRFT)对LFM信号的能量聚焦特性,构造出一种新的FRFT域阵列数据模型;采用UCA-RB-MUSIC算法测向,通过模式激励法把阵元空间转换到实波束空间,对谱函数进行二维搜索,得到辐射源的方位角和俯仰角.通过理论推导和仿真验证,证明方法具有测向精度高、运算量小、360°全方位测向的优点.     

高精度低复杂度的无线定位新方法

针对高精度的无线定位算法普遍存在运算量较大的问题,提出了一种二维波束空间矩阵束算法进行波达时间（TOA）和波达方向（DOA）联合估计,能够以较低的复杂度准确定位目标。该算法先通过离散傅里叶变换（DFT）波束形成矩阵将阵元空间的接收数据复数矩阵变换成波束空间的降维实数矩阵,使得运算量大幅度降低;再通过奇异值分解和求矩阵对的广义特征值估计视距信号TOA和DOA,从而确定目标位置。Matlab仿真实验结果证明,这种定位方法的均方根误差最好达到0.4m,运算量不到阵元空间对应算法的1/4,是一种高精度低复杂度的无线定位方法,尤其适用于资源有限的特殊环境（如战场、地震灾区、偏远山区等）中的无线网络定位。     

高精度低复杂度的无线定位新方法

针对高精度的无线定位算法普遍存在运算量较大的问题,提出了一种二维波束空间矩阵束算法进行波达时间(TOA)和波达方向(DOA)联合估计,能够以较低的复杂度准确定位目标。该算法先通过离散傅里叶变换(DFT)波束形成矩阵将阵元空间的接收数据复数矩阵变换成波束空间的降维实数矩阵,使得运算量大幅度降低;再通过奇异值分解和求矩阵对的广义特征值估计视距信号TOA和DOA,从而确定目标位置。Matlab仿真实验结果证明,这种定位方法的均方根误差最好达到0.4 m,运算量不到阵元空间对应算法的1/4,是一种高精度低复杂度的无线定位方法,尤其适用于资源有限的特殊环境(如战场、地震灾区、偏远山区等)中的无线网络定位。     

复杂电磁网络环境下的抗干扰技术研究与仿真

在完成复杂网络环境下抗干扰的过程中,各种干扰信号构成的混合信号极为复杂,当前的有关信息最大化的复杂电磁网络环境下抗干扰方法,仅能将复杂信号分离成超高斯分布或亚高斯函数分布信号,无法进一步细化,不能实现复杂网络环境下的抗干扰,提出一种关于波束赋形技术的复杂电磁网络环境下的抗干扰方法,从时域与频域两个角度分析复杂电磁网络环境信号;依据波束形成对空间传感器的采样加权进行求和操作,提高某一特定方向传播波信号,避免其它方向的干扰.对来波方向和阵列法线方向的夹角进行定义,形成波束后的输出信号,给出阵列的方向矩阵以及方向向量,利用Bulter变换矩阵完成阵元域到波束域之间的转换.仿真结果表明,所提方法具有很高的抗干扰能力.     

一种新的矢量传感器线列阵波束形成算法

为了提高基于矢量线列阵的目标方位估计能力,将基于时域解析信号实现最小方差无畸变响应（ MVDR）的方法——TAMVDR算法引入到了矢量线列阵信号处理中,提出了实现矢量线列阵波束形成的VTAMVDR算法。理论分析了矢量线列阵VTAMVDR算法的原理,该算法通过Hilbert变换对时域宽带信号引入复权向量,不需要进行子带分割,且不需要对数据进行分块处理,获得稳定优化权向量估计所需要的数据长度远小于频域MVDR方法,数据长度合适时,单次快拍即可实现波束形成,大大降低了运算量。仿真和海上试验数据分析结果表明：VTMVDR算法相比于频域MVDR算法具有较好的性能,具有更高的分辨率和更窄的波束角,有更好的探测性能。     

Adaptive sonar beamformer based on inverse QR decomposition and recursive least squares filter for underwater target detection

To enhance underwater target detection performance, a standard hexagonal array (HA) (plane array) is designed for active sonar implementation in shallow water environments. For the hexagonal receiving array, the numerically robust inverse QR (Q, orthogonal matrix; R, upper triangular matrix) decomposition and recursive least-squares (RLS) are used to derive the minimum variance distortionless response (MVDR) beamformer (BF) under a hexagonal fast Fourier transform (HFFT) framework. The HFFT inverse QR (IQR)-RLS algorithm offers computational saving and can be mapped onto coordinate rotation digital computer processor-based systolic arrays, which makes it suitable for array real-time application. An analysis of the numerical robustness and computational complexity of the adaptive beamforming is presented. Using the proposed scheme to build HA adaptive BF reduces the computational burden and offers a better convergence rate than conventional BF. The experimental data analysis demonstrates the effectiveness of the algorithm against reverberation interference, and its improvement of target localization accuracy in a reverberation-limited area during the underwater target detection process.     

Five-step FFT algorithm with reduced computational complexity

We propose a fast Fourier transform algorithm, which removes two steps of twiddle factor multiplications from the conventional five-step FFT algorithm. The proposed FFT algorithm not only reduces the computational complexity of the five-step FFT algorithm by O(n) operations, but also reduces its memory requirement.     

基于FFT的子孔径MUSIC波达方向估计

针对现 有的很多波达方向估计算法涉及到数据协方差矩阵的估计及其特征分解,甚至是求逆,导致 运算复杂度高的问题,提出了基于快速傅里叶变换的子孔径MUSIC波达方向估计算法 。首先将等距线阵的接收数据矢量均匀划分为4个子矢量,然后对各个子矢量分别求FFT。将 FFT的结果相干积累,并找到最大峰值点。最后,利用子矢量FFT的结果中与最大峰值点对应 的数据构造新的降维矢量,借助MUSIC算法进行波达方向估计。该方法避免了直接接收数据 的协方差矩阵估计和特征分解,有效地降低了运算量和计算复杂度,在阵元数和快拍数都较 多的情况下优越性尤为明显。计算机仿真验证了所提方法的有效性和优越性。     

基于频域ICA的波达方向估计方法

为降低阵元数目和提高相干多径入射信号的波达方向(DOA)估计精度。提出了一种基于频域独立分量分析与波束零点形成相结合的DOA估计方法。该方法综合利用阵列结构信息和目标信号的统计独立特性,与常规算法相比,降低了算法对阵元数目和精度的依赖,并能实现对相干多径入射信号的DOA估计。计算机仿真结果表明,该算法具有少阵元、收敛快、误差小的特点。     

频域宽带阵列波束形成技术优化设计

为提高宽带相控阵系统的波束合成性能,该文针对宽带相控阵系统中的延时补偿问题,采用频域宽带阵列波束形成的方法,分析了宽带相控阵中应用交叠FFT进行时延补偿的原理和误差造成的原因;基于一个接收信号带宽为600MHz的64阵元的宽带相控阵系统,研究了子阵规模、FFT点数、交叠率、位宽、采样率等交叠FFT参数对延时精度、信号保真度和波束性能的影响,在满足工程应用的要求的同时对频域宽带阵列波束合成技术进行了优化;经研究确定子阵规模不超过9个天线阵元、FFT点数不小于512、交叠率不小于1/16、位宽不小于采用12bit时可以达到指标的要求,为交叠FFT方法应用在实际工程中提供了依据与参考,并使其工程实现复杂度降低。     

Fast parallel algorithms for discrete Gabor expansion and transform based on multirate filtering

The Gabor transform has long been recognized as a very useful tool for the joint time and frequency analysis in signal processing.Its real time applications,however,were limited due to the high computational complexity of the Gabor transform algorithms.In this paper,some novel and fast parallel algorithms for the finite discrete Gabor expansion and transform are presented based on multirate filtering.An analysis filter bank is designed for the finite discrete Gabor transform(DGT)and a synthesis filter bank is designed for the finite discrete Gabor expansion(DGE).Each of the parallel channels in the two filter banks has a unified structure and can apply the FFT and the IFFT to reduce its computational load.The computational complexity of each parallel channel does not change as the oversampling rate increases.In fact,it is very low and depends only on the length of the input discrete signal and the number of the Gabor frequency sampling points.The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the major existing parallel algorithms for the finite DGT and DGE.The results indicate that the proposed parallel algorithms for the finite DGT and DGE based on multirate filtering are very attractive for real time signal processing.     

Fast Fourier Transform for Hexagonal Aggregates

Hexagonal aggregates are hierarchical arrangements of hexagonal cells. These hexagonal cells may be efficiently addressed using a scheme known as generalized balanced ternary for dimension 2, or GBT₂. The objects of interest in this paper are digital images whose domains are hexagonal aggregates. We define a discrete Fourier transform (DFT) for such images. The main result of this paper is a radix-7, decimation-in-space fast Fourier transform (FFT) for images defined on hexagonal aggregates. The algorithm has complexity N log₇ N. It is expressed in terms of the p-product, a generalization of matrix multiplication. Data reordering (also known as shuffle permutations) is generally associated with FFT algorithms. However, use of the p-product makes data reordering unnecessary.     

Fast hyperbolic Radon transform using chirp-z transform

The hyperbolic Radon transform plays an important role in seismic data processing for its ability to focus seismic events in the transform domain. Traditional algorithms based on direct implementations, however, are inefficient with limited applications for processing large data sets. A new algorithm is presented for fast computation of the hyperbolic Radon transform and its sparse calculations. It uses interpolation procedures to stretch the data along time axis and efficiently computes the summation paths in the new coordinates via the chirp-z transform which is carried out by fast Fourier transform (FFT). The proposed fast algorithm is then used within the deconvolutive form of the Radon transform and iterative sparse algorithms for effective decomposition of CMP gathers with an improved temporal resolution, compared to the traditional Radon transforms. The effectiveness of the new algorithm are confirmed on sparse velocity-stack inversion, primary and multiple separation, high-quality stacking, and automatic velocity model building. The tests show that sparse velocity-stack inversion using the new algorithm is even more efficient than the traditional velocity scan, both in resolution and speed. Furthermore, numerical tests show the superiority of the proposed algorithm over the state-of-the-art fast algorithms, based on butterfly scheme and log-polar convolutions, demanding less computational complexity.     

The Partial Fast Fourier Transform

An efficient algorithm for computing the one-dimensional partial fast Fourier transform \(f_j=\sum _{k=0}^{c(j)}e^{2\pi ijk/N} F_k\) is presented. Naive computation of the partial fast Fourier transform requires \({\mathcal O}(N^2)\) arithmetic operations for input data of length N. Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on the space variable j; this prevents one from directly applying standard FFT algorithms. It is shown that the space–frequency domain can be partitioned into rectangular and trapezoidal subdomains over which efficient algorithms can be developed. As in the previous work of Ying and Fomel (Multiscale Model Simul 8(1):110–124, 2009), the contribution from rectangular regions can be reduced to a series of fractional-phase Fourier transforms over squares, each of which can be reduced to a convolution. In this work, we demonstrate that the partial Fourier transform over trapezoidal domains can also be reduced to a convolution. Since the computational complexity of a dealiased convolution of N inputs is \({\mathcal O}(N\log N)\), a fast algorithm for the partial Fourier transform is achieved, with a lower overall coefficient than obtained by Ying and Fomel.