傅氏窗函数与小波变换

本文介绍了两种可同时进行时空域分析和频率域分析的分解－加窗傅氏变换和小波变换。通过对比，我们可以更好地了解这两种分解的性质和特点，并进一步体现出小波变换的优越性。     

基于滑动时窗的小波变换实时算法

本文针对基于滑动时窗的小波变换中小波系数重复计算的问题,通过预先存储一部分小波系数,避免重复计算过程,以较小的存储空间为代价,获得了计算效率很高的小波变换实时算法,且小波变换实时算法获得的小波系数与多孔算法计算得到的小波系数完全相同。仿真结果表明:基于滑动时窗的小波变换实时算法快速、稳定,是一种值得推广使用的高效算法。     

DMBT系统中利用FWT快速实现信道估计

根据PN码的结构特性,针对DMB-T系统多载波模式,本文提出了一种新的理论上与滑窗相关法等价的信道估计方法,利用FWT(快速沃尔什变换)实现快速多径捕获.通过干扰抵消进一步消除了径间干扰.该方法具有很强的抗多径效应和抗强窄带干扰的能力,将运算复杂度从传统滑动互相关法的N~2降低到(N+1)log_2(N+1).     

多分量信号快速时频分析方法

针对目前多分量时频分析方法计算复杂度高,难以实现持续信号实时处理的问题,提出一种多分量信号快速时频分析方法。该方法通过信号流逐窗时频变换,实现信号的快速时频分析,其主要计算过程为短时傅立叶变换,时间和空间复杂度低,易于工程实现。性能分析结果表明:该方法时频分辨率高,避免了交叉项干扰,能有效分析低信噪比信号。     

基于三维变换域频谱差的视频显著性检测算法

显著性区域检测是计算机视觉的重要课题,对视频质量评价和感知视频编码算法优化也至关重要.大多显著性检测算法不能权衡准确率和复杂度,限制了它们在视频预处理和实时处理中的应用.提出了一种基于三维变换域频谱差(3DTDSD)的快速视频显著性检测算法,分别以关键帧及其前一帧为中心建立一定数量图像帧的滑动窗,得到两组3D视频体,用傅里叶变换将两组视频变换到三维频域,两组三维数据之间的差值经过反变换得到显著性图,最后通过连通分析、阈值判断等得到显著区域.频域算法具有运算速度快的特点,实验对比和算法复杂度分析证明了该算法的有效性和快速性.     

AR谱估计的一种自适应算法

本文给出Householder变换的一种实时递推算法及其收敛性证明,并用此算法进行AR自适应谱估计。仿真计算表明,此算法具有计算结果准确、可以实时判阶和快速跟踪性好等特点。     

快速傅立叶变换辅助设计数字低通滤波器

详尽讨论了快速傅立叶变换(FFT)应用于有限冲击响应(FIR)数字低通滤波器(DLPF)的设计和分析方法.应用FFT算法,将理想DLPF幅频特性转换到变换域,获得其变换域序列;设计窗函数对该序列开窗,获得FIR有限序列;应用快速傅立叶逆变换(IFFT)对其进行变换,获得相应窗函数可实现DLPF幅频特性.结果发现,FFT算法可获得与传统卷积算法相同的结果;不需要推算窗函数的频谱解析表达式;可以处理Kaiser窗等变换域解析式复杂、频域解析式难以精确求解的窗函数设计与分析.与传统的卷积分析法相比,FFT不仅算法简单、灵活,而且处理能力强,是分析FIR DLPF设计的有力工具.     

自适应短时傅立叶变换算法的研究

详细分析了窗函数选择对短时傅立叶变换的影响,提出了一种窗长自适应的短时傅立叶变换算法,并给出了快速算法,进行了算法复杂度分析,最后给出了仿真实验。     

利用稀疏傅里叶变换的哈希映射法的宽带频谱感知算法

宽带频谱感知一般要求对高达数 GHz带宽信号进行频谱分析,信号的采样点数大,计算量大。稀疏傅里叶变换算法利用信号频谱稀疏性,高效计算宽带信号频谱,其计算复杂度低于快速傅里叶变换算法。本文详细研究了稀疏傅里叶变换的哈希映射法,证明了频谱重排性质。为了降低频谱漏采的概率,需先对信号进行频谱重排和时域加窗处理;然后进行时域混叠以实现频谱降采样;最后利用哈希反映射和循环投票方法尽可能准确地从降采样的频谱中恢复宽带信号原频谱,从而实现频谱感知。仿真结果表明当采样长度由1024点增加到2048点时,本文方法的运算时间分别比OMP算法减少约19倍和47倍。      

大型阵列结构电磁散射的P-FFT算法

提出利用预校正的快速傅立叶变换(P-FFT)和矩量法(MoM)快速分析电大阵列结构的电磁散射特性.研究了适合于电大尺寸结构近区和远区场计算的格林函数的快速算法,同时,利用Rao-Wilton-Glisson(RWG)函数作为基函数和测试函数,可以考虑阵列单元任意方向的表面电流或磁流分布,并利用P-FFT加速矩量法的矩阵求解,减少内存需求和计算时间.计算结果表明该方法特别适合于大型阵列电磁散射特性的分析.     

Complete Gabor transformation for signal representation

Properties of the Gabor transformation used for image representation are discussed. The properties can be expressed in matrix notation, and the complete Gabor coefficients can be found by multiplying the inverse of the Gabor (1946) matrix and the signal vector. The Gabor matrix can be decomposed into the product of a sparse constant complex matrix and another sparse matrix that depends only on the window function. A fast algorithm is suggested to compute the inverse of the window function matrix, enabling discrete signals to be transformed into generalized nonorthogonal Gabor representations efficiently. A comparison is made between this method and the analytical method. The relation between the window function matrix and the biorthogonal functions is demonstrated. A numerical computation method for the biorthogonal functions is proposed.     

一种改进的滑动窗FFT递推算法

在信号谱线分析中,经常用到滑动窗的FFT计算,由于传统的FFT在N值较大和滑动步进较小时,计算量较大,在实时通信系统中难以实现,本文提出一种连续滑动窗的递推FFT算法,该算法充分利用了前窗的计算结果并将输入序列转换为一个输入端仅有少数非零点的特殊序列,不仅降低了计算量,而且提高了使用的灵活性和实时性。     

基于Gabor变换的数字通信信号调制盲识别

Gabor变换通过加窗函数的办法对Fourier变换加以改进，能较好地刻画信号中的瞬态结构。本文把Gabor变换引入到了数字通信信号调制盲识别领域，对ASK、FSK和PSK信号的Gabor变换域特征进行了理论分析和软件仿真，最后给出了识别算法和仿真结果。     

基于自适应滑窗递归稀疏主成分分析的工业过程故障监测

本文提出一种自适应滑窗递归稀疏主成分分析方法,用于时变工业过程的在线故障监测.首先,通过滑窗提取正常过程数据空间的特征信息,并对当前窗口数据块矩阵进行稀疏主成分分析,构建稀疏主成分分析故障监测模型;然后,根据相邻窗口的相似度实时调整遗忘因子以自适应更新滑窗大小,使得所建立的稀疏主成分故障监测模型可以有效追踪复杂的时变过程;最后,通过递归更新滑窗稀疏载荷矩阵来动态更新故障监测模型.非线性数值仿真系统与田纳西-伊斯曼过程的故障监测结果表明,所提方法可以有效提高故障检测的准确率,适应于长流程时变工业过程在线故障监测.     

变窗Gabor变换理论及其在图像处理中的应用

基于Ｇａｂｏｒ变换和小波变换提出了变窗Ｇａｂｏｒ变换，讨论了它它的若干优良特性。变窗Ｇａｂｒｏ变换包含了Ｆｏｕｒｉｅｒ变换，Ｇａｂｏｒ变换，波变换的一般化，基于上述变换对变窗Ｇａｂｏｒ变换提出了不同的快速算法。     

Optimal tracking of time-varying channels: a frequency domainapproach for known and new algorithms

In this paper, we developed a systematic frequency domain approach to analyze adaptive tracking algorithms for fast time-varying channels. The analysis is performed with the help of two new concepts, a tracking filter and a tracking error filter, which are used to calculate the mean square identification error (MSIE). First, we analyze existing algorithms, the least mean squares (LMS) algorithm, the exponential windowed recursive least squares (EW-RLS) algorithm and the rectangular windowed recursive least squares (RW-RLS) algorithm. The equivalence of the three algorithms is demonstrated by employing the frequency domain method. A unified expression for the MSIE of all three algorithms is derived. Secondly, we use the frequency domain analysis method to develop an optimal windowed recursive least squares (OW-RLS) algorithm. We derive the expression for the MSIE of an arbitrary windowed RLS algorithm and optimize the window shape to minimize the MSIE. Compared with an exponential window having an optimized forgetting factor, an optimal window results in a significant improvement in the h MSIE. Thirdly, we propose two types of robust windows, the average robust window and the minimax robust window. The RLS algorithms designed with these windows have near-optimal performance, but do not require detailed statistics of the channel     

基于DCT的实值离散Gabor变换

该文提出了一种基于离散余弦变换(DCT)的实值离散Gabor变换(RDGT),不仅适用于临界抽样条件而且适用于过抽样条件,并证明了变换的完备性条件。由于这种变换仅涉及实值计算,并且可利用快速DCT,IDCT算法来加速运算,因此比传统复值离散Gabor变换在计算和实现方面更为简单,必将有效地提高非平稳信号与图像的分析、处理速度和效率。     

A fast learning algorithm for Gabor transformation

An adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2-D Gabor (1946) transform representation is introduced. The algorithm uses a recursive least squares (RLS) type algorithm. The aim is to achieve minimum mean squared error for the reconstructed image from the set of the Gabor coefficients. The proposed RLS learning offers better accuracy and faster convergence behavior when compared with the least mean squares (LMS)-based algorithms. Applications of this scheme in image data reduction are also demonstrated.     

利用RPLS算法实现电力系统频率跟踪

针对在电力系统频率跟踪算法中推导过程复杂、计算量大等问题,提出了一种利用递推偏最小二乘法(RPLS)实现电力系统频率跟踪的新算法。该方法在递推过程中,采用滑动窗法更新数据,同时引入了适当的遗忘因子。仿真结果表明,该算法在电力系统频率跟踪中具有计算复杂度小,推导过程简单,频率跟踪收敛速度快,测量精度高的特点,其是电力系统频率跟踪中的一种新方法。     

Novel DCT-Based Real-Valued Discrete Gabor Transform and Its Fast Algorithms

The oversampled Gabor transform is more effective than the critically sampled one in many applications. The biorthogonality relationship between the analysis window and the synthesis window of the Gabor transform represents the completeness condition. However, the traditional discrete cosine transform (DCT)-based real-valued discrete Gabor transform (RGDT) is available only in the critically sampled case and its biorthogonality relationship for the transform has not been unveiled. To bridge these important gaps, this paper proposes a novel DCT-based RDGT, which can be applied in both the critically sampled case and the oversampled case, and their biorthogonality relationships can be derived. The proposed DCT-based RDGT involves only real operations and can utilize fast DCT algorithms for computation, which facilitates computation and implementation by hardware or software as compared to that of the traditional complex-valued discrete Gabor transform. This paper also develops block time-recursive algorithms for the efficient and fast computation of the RDGT and its inverse transform. Unified parallel lattice structures for the implementation of these algorithms are presented. Computational complexity analysis and comparisons have shown that the proposed algorithms provide a more efficient and faster approach for discrete Gabor transforms as compared to those of the existing discrete Gabor transform algorithms. In addition, an application in the noise reduction of the nuclear magnetic resonance free induction decay signals is presented to show the efficiency of the proposed RDGT for time-frequency analysis.