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。     

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。     

基于实值离散Gabor变换的联合时频域语音增强

传统变换域语音增强方法对语音做短时平稳性假设,这会造成对语音信号和噪声信号谱估计不准确,从而导致语音失真和残留噪声。本文提出一种从联合时频域进行语音增强的方法,该算法无需对语音做短时平稳假设。算法采用具有最佳能量聚集特性的高斯变换核函数,利用能快速实现的实值离散Gabor变换（RDGT）将语音信号变换到联合时频域,然后利用语音和噪声谱服从高斯分布的假设和无语音概率的思想进行基于最小均方误差的语音对数谱估计,采用改进的最小受控递归平均算法（IMCRA）进行噪声时频谱估计,在得到纯净语音的谱估计后利用实值离散Gabor逆变换获得纯净语音估计。实验表明,该算法相比频域变换算法具有较好的语音去噪度和较低的语音失真度。      

DGT与DCT在图像编码中的性能比较

介绍了二维实值离散Gabor变换（RDGT）的快速算法,并着重探讨了二维实值离散Gabor变换与二维离散余弦变换在图像编码中的性能及差异。     

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...     

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。     

任意长度的离散W变换的一种递归算法

离散W变换(DWT)在数字信号和图像处理领域有着广泛的应用.由于其涉及的计算的复杂性,众多学者提出了诸多DWT的快速算法来降低计算复杂度和硬件复杂度.本文针对任意长度的序列提出一种新的计算DWT的递归方法.我们利用Clenshaw 递归关系式推导了一种可以有效计算II型,III型和IV型DWT系数的递归算法.结果表明,该算法不仅结构简单,而且非常适合采用VLSI来并行实现.     

最佳递归傅里叶变换算法

本文阐述了离散傅里叶变换的递归算法。表明当变换长度N=P是一个质数时,算法就变得特别简单,只要用一个复数系数W_P~D就可以计算全部N个频率分量。本文讨论了系数选择与信噪比的关系。求出了递归算法的最佳系数,这些系数使得定点实现傅里叶交换时具有最大信号噪声比。     

递归算法的参数设置

提出了基于循环迭代运算的多路并行递归算法,代替传统的快速傅立叶变换(FFT)算法,进行有限长数据的离散傅立叶变换(DFT)。递归算法具有数据存储量少、计算量小、资源占用量与工作参数变化无关等特点。计算机仿真结果表明:递归算法不仅使所分析的频率在频率轴上可以选择任意实数值,而且时间分辨率和频率分辨率可调可控。递归算法的工作参数可以依据战术环境灵活设置与调整,非常适合对局部频段实时地进行信号检测、时频分析和精确的时、频参数测量,也可以和其它已有的算法配合使用。     

二维实值离散Gabor变换与DCT在图像编码中性能的比较

介绍了二维实值离散Gabor变换（RDGT）的快速算，并着重探讨了二维实值离散Gabor变换与二维离散余弦变换在图像编码中的性能及差异。     

Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.     

Fast Parallel Approach for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.      

Multirate-based fast parallel algorithms for DCT-kernel-based real-valued discrete Gabor transform

Fast parallel algorithms for the DCT-kernel-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented based on multirate signal processing. An analysis convolver bank is designed for the RDGT and a synthesis convolver bank is designed for its inverse transform. The parallel channels in each of the two convolver banks have a unified structure and can apply the fast DCT algorithms to reduce computation. The computational complexity of each parallel channel is low and depends mainly on the length of the discrete input signal and the number of the Gabor frequency sampling points. Every parallel channel corresponds to one RDGT coefficient, and all the RDGT coefficients are computed in parallel during the analysis process and are finally reconstructed in parallel as pieces of the original signal during the synthesis process. The computational complexity related to the computational time of each RDGT coefficient or each piece of the reconstructed signal in the proposed parallel algorithms is analyzed and compared with those in the existing major parallel algorithms for the RDGT and its inverse transform. The results indicate that the proposed multirate-based fast parallel algorithms for the RDGT are attractive for real-time signal processing.     

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.      

An efficient algorithm to compute the complete set of discreteGabor coefficients

The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discrete Gabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients. The similarity of the formulas between the discrete Gabor transform and the discrete Fourier transform enables one to employ the FFT algorithms in the computation. The discrete 1-D Gabor transform algorithm can be extended to 2-D as well.     

用于语音分析的实值离散GABOR变换

提出了语音信号的快速实值离散Gabor变换（RDGT）方法,讨论了由RDGT系数计算语音复谱图值、语谱图生成和语音信号的快速重建问题。并给出了实例。     

Split-Radix Algorithms for Arbitrary Order of Polynomial Time Frequency Transforms

The polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial-phase signals (PPSs) with the maximum likelihood method. The transform converts a one-dimensional (1-D) data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated. A prohibitive computational load is generally needed for high-order polynomial-phase signals although the 1-D fast Fourier transform (FFT) algorithm can be used. Based on the split-radix concept, this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity. Comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm     

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.