Zak变换在Gabor展开理论中的应用

利用离散Zak变换及其性质,本文首次给出了在过采样条件下,频域离散Gabor展开系数与时域离散Gabor展开系数之间的简捷关系,这对Zak变换的应用和完善Gabor展开理论是很有意义的,论文最后给出了计算实例。     

基于离散傅里叶变换和块时间递归并行格型结构的离散Gabor分析窗求解

提出了一种快速求解离散Gabor变换分析窗的方法.首先选择一个合适的基函数,同给定的综合窗函数构造一个可逆的块循环矩阵,然后根据块循环矩阵特点,利用快速离散傅里叶变换求解块循环矩阵的逆,最后采用基于块时间递归的并行格型结构来求解分析窗.本文证明了此算法获得的窗函数与给定的综合窗满足双正交关系.实验结果表明,本文算法能快...     

数字信号处理中的滑窗表示

离散时间信号的短时付里叶变换解释为滑窗谱,它是信号加窗后的付氏变换。这种滑窗谱是两个变量的函数:一是离散时间指数,它表示窗口的位置;二是连续频率变量.文章证明了信号可以由取样了的滑窗谱重建,也就是由滑窗谱在特定的时间频率域中点阵上各点的值来重建。取样点阵是矩形的,矩形元素在时间频率域上的面积为2π。本文证明,一种直接根据滑窗谱的取样值来表示信号的精微方法是Gabor 信号表示法。为此引入了互易窗的概念,并且阐明了窗和互易窗是怎样联系在一起的,Gabor 信号表示法将信号表示成由互易窗经适当移位和调制以后的展开式,展开系数就是取样了的滑窗谱的值。     

二维实值离散Gabor变换时间递归算法的双层并行格型结构实现方法

本文首先简单回顾了作者曾提出的二维实值离散Gabor变换及其与复值离散Gabor变换的简单关系，然后着重探讨了二维实值离散Gabor变换快速计算问题，提出了二维实值离散Gabor变换系数求解的时间递归算法以及由变换系数重构原图像的块时间递归算法，研究了双层并行格型结构实现算法的方法，计算复杂性分析及与其它算法的比较证明了双层并行格型结构实现方法在实时处理方面的优越性。     

实值离散Gabor变换块时间递归算法的并行格型结构实现方法

Gabor变换在很多领域被认为是非常有用的方法,如语音与图像处理,雷达、声纳、振动信号的处理与理解等,然而实时应用却因其很高的计算复杂性而受到限制.为了减小计算复杂性,我们曾提出了实值离散Gabor变换法.本文首先简单回顾了作者曾提出的实值离散Gabor变换及其与复值离散Gabor变换的关系,然后为了有效地和快速地计算实值离散Gabor变换,提出了在临界抽样条件下和在过抽样条件下,一维实值离散Gabor变换系数求解的块时间递归算法以及由变换系数重建原信号的块时间递归算法,研究了两算法使用并行格型结构的实现方法,并讨论和比较了算法的计算复杂性和优越性.     

拟正交Gabor展开的构造

利用Ｚａｋ变换和框架作为数学工具，本文给出了一种在整数倍过抽样时构造拟正交Ｇａ－ｂｏｒ展开的方法。由于拟正交Ｇａｂｏｒ展开的窗函数及对偶窗具有相同的形式，使得Ｇａｂｏｒ展开的计算特别简单。由于所构造的窗函数具有良好的时频局部特性，在计算机视觉和信号处理等领域有着广泛的应用前景     

基于对偶理论的多点协同联合发送波束成形算法

该文针对单基站功率约束的多点协同联合发送多输入单输出干扰下行链路系统,利用拉格朗日对偶理论研究了下行链路最大化最小信干噪优化问题与虚拟上行链路最小化最大信干噪比优化问题间的对偶关系。基于对偶关系和次梯度理论,提出了一种求解虚拟上行链路最小化最大信干噪比优化问题的内外层交替迭代优化波束成形算法;同时,给出了所提算法的收敛性证明;利用实数浮点运算理论分析了所提算法的复杂度;数值仿真验证了所提算法的有效性。     

离散Gabor展开及其关系

Ｇａｂｏｒ 展开是一种分析非平稳信号的工具。为了能进行数值计算,需要对连续 Ｇａｂｏｒ展开进行离散化和有限化。在过采样的一般情况下,给出了有限离散时域 Ｇａｂｏｒ 展开系数与有限离散频域 Ｇａｂｏｒ 展开系数之间的关系,并给出了一个计算实例。     

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。     

连续Gabor展开离散化后的混叠问题

为能进行数值计算，需对连续Ｇａｂｏｒ展开离散化有限化。本文就时域与频域两种情况，给出了在过采样率的一般情况下，有限离散化后的Ｇａｂｏｒ展开系数与原连续Ｇａｂｏｒ展开系数之间的关系，并由此推出了离散Ｇａｂｏｒ展开系数不产生混叠的条件——连续Ｇａｂｏｒ展开离散化的采样定理。最后给出了一个计算实例     

The generalized Gabor transform

The generalized Gabor transform (for image representation) is discussed. For a given function f(t), tinR, the generalized Gabor transform finds a set of coefficients a(mr) such that f(t)=Sigma(m=-infinity)(infinity)Sigma (r=-infinity)(infinity)alpha(mr )g(t-mT)exp(i2pirt/T'). The original Gabor transform proposed by D. Gabor (1946) is the special case of T=T'. The computation of the generalized Gabor transform with biorthogonal functions is discussed. The optimal biorthogonal functions are discussed. A relation between a window function and its optimal biorthogonal function is presented based on the Zak (1967) transform when T/T' is rational. The finite discrete generalized Gabor transform is also derived. Methods of computation for the biorthogonal function are discussed. The relation between a window function and its optimal biorthogonal function derived for the continuous variable generalized Gabor transform can be extended to the finite discrete case. Efficient algorithms for the optimal biorthogonal function and generalized Gabor transform for the finite discrete case are proposed.     

离散拟正交GaBor展开

利用一般条件的离散Ｚａｋ变换及连续Ｇｏｂｏｒ展开和离散Ｇａｂｏｒ展开间的关系。本文首次提出了在整数倍过抽样条件下，由Ｗｅｙｌ－Ｈｅｉｓｅｎｂｅｒｇ紧框架构造离散ＧＡＢＯＲ展开的方法。     

Discrete Gabor transform

A feasible algorithm for implementing the Gabor expansion, the coefficients of which are computed by the discrete Gabor transform (DGT), is presented. For a given synthesis window and sampling pattern, computing the auxiliary biorthogonal function of the DGT is nothing more than solving a linear system. The DGT presented applies for both finite as well as infinite sequences. By exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like DGT is obtained. As the discrete Fourier transform (DFT) is a discrete realization of the continuous-time Fourier transform, similarly, the DGT introduced provides a feasible vehicle to implement the useful Gabor expansion     

The undersampled discrete Gabor transform

Conventional studies on discrete Gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the Gabor families span the whole signal space. In this paper, we investigate undersampled discrete Gabor transforms. For an undersampled Gabor triple (g,a,b), i.e. a·b>N, we show that the associated generalized dual Gabor window (GDGW) function is the same as the one associated with the oversampled (g,N/b,N/a), except for the constant factor (ab/N). Computations of undersampled Gabor transforms are made possible. By applying the methods (algorithms) developed in oversampled settings, the undersampled GDGW is determined. Then, we are able to obtain the best approximation of a signal x by linear combinations of vectors in the Gabor family     

实值离散GABOR变换的最优双正交分析窗函数

Ｇａｂｏｒ变换在信号图像处理中是一非常有用的工具。本文首先回顾了作者曾提出的实值离散Ｇａｂｏｒ变换方法,然后着重讨论了在已知综合窗函数条件下,双正交分析窗函数的最优解问题,指出在许多情况下,这些最优解（如最小范数解与最似正交解）都是相同的,并讨论了采用奇异值分解（ＳＶＤ）理论求解双正交分析窗函数的方法。文末还给出了求解了实例。     

临界抽样Gabor展开的非局部性分析

Ｇａｂｏｒ展开是一在时－频混合空间描述信号的非正交展开。由于展开的非正交性，使得展开系数的计算较为困难。现有的关于Ｇａｂｏｒ展开的文献大都集中在讨论Ｇａｂｏｒ展开的计算，而对临界抽样Ｇａｂｏｒ展开的非局部性问题没有给予足够的重视。本文将证明当临界抽样Ｇａｂｏｒ展开的窗函数为连续或对称函数时，Ｇａｂｏｒ展开不仅存在非局部性问题，而且收敛性也得不到保证。同时我们还将给出临界抽样Ｇａｂｏｒ展开非局部性的     

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.      

A discrete fractional Gabor expansion for multi-component signals

Gabor expansion is widely used to represent the time-varying frequency content of non-stationary signals. Recently, new representations are presented on a general non-rectangular time–frequency grid. In this paper, we present a closed-form, discrete fractional Gabor expansion and show that it can be used to estimate a high resolution time–frequency representation for multi-component signals. The proposed expansion uses the discrete fractional Fourier kernel and generates a parallelogram-shaped time–frequency plane tiling. Completeness and biorthogonality conditions of the new expansion are derived. We also present a search algorithm to obtain optimal analysis fraction orders for the compact representation of multi-component signals.