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1.
本文以DFT的收缩(Systolic)阵列结构为基础,给出了一类数字变换的收缩阵列,这些变换包括离散富里叶变换,离散余弦变换,离散正弦变换,离散Hartley变换,数论变换和多项式变换.  相似文献   

2.
任意长度离散余弦变换的快速算法   总被引:2,自引:0,他引:2  
曾泳泓 《计算数学》1993,15(3):295-302
§1.引言 离散余弦变换(DCT)有趋于统计最佳交换Kavhunven-Lave变换(KLT)的渐近性质,在通信和信号处理中应用广泛,并在许多方面比离散富里叶变换(DFT)更好。  相似文献   

3.
为了提高块压缩感知的测量效率和重构性能,根据离散余弦变换和离散正弦变换具有汇聚信号能量的特性,提出了基于重复块对角结构的部分离散余弦变换(partial discrete cosine transform in repeated block diagonal structure,PDCT-RBDS)和部分离散正弦变换(partial discrete sine transform in repeated block diagonal structure,PDST-RBDS)的两种压缩感知测量方法.所采用的测量矩阵是一种低复杂度的结构化确定性矩阵,满足受限等距性质.并得到一个与采样能量有关的受限等距常数和精确重构的测量数下限.通过与采用重复块对角结构的部分随机高斯矩阵和部分贝努利矩阵的图像压缩感知对比,结果表明,PDCT-RBDS和PDST-RBDS重构的PSNR大约提高1~5 dB,SSIM提高约0.05,所需的重构时间和测量矩阵的存储空间大大减少.该方法特别适合大规模图像压缩及实时视频数据处理场合.  相似文献   

4.
1 引 言 Ⅱ型离散余弦变换(DCT—Ⅱ)有超于统计最佳变换Karhunen—Loeve变换(KLT)的渐近性质,因而在通信和信号处理中得到了广泛应用,尤其是在图像处理中它是最有用的变换。设x(k)(k=0,1,…,N—1)为实数序例,其DCT—Ⅱ的定义为 X(n)=sum from k=0 to N-1 x(k)cos(π(2k+1)n)/2N,n=0,1,…,N-1。 (1)  相似文献   

5.
偏积分微分方程产生于许多科学与工程领域,数值求解此类问题具有重要应用.本文给出了数值求解一类长时间偏积分微分方程的二阶差分空间半离散格式.借助于Laplace变换及Parseval等式,给出了全局稳定性的证明、误差估计及全局收敛性的结果.  相似文献   

6.
本文讨论了R^空间中正交变换及正交矩阵的性质.按照计算机演示-大胆猜想-理论证明的步骤,解决了正交变换迭代向量的分布问题.最后通过基变换将正交变换分为四类,并分别论证了其变换形式与特征值的关系.  相似文献   

7.
欧氏空间三种变换之间的关系   总被引:2,自引:0,他引:2  
邹本强 《数学通报》1999,(5):41-41,24
在[1]中,我们了解了欧氏空间的两类重要的线性变换,一类是正交变换,一类是对称变换.本文给出另外两类线性变换,一类是反对合变换,另一类是反对称变换,指出正交变换、反对称变换,反对合变换三种变换之间的关系.本文术语及符号同[1].定义1数域F上的n维向...  相似文献   

8.
本文给出了可积离散的NLS 方程的贝克朗变换 ,并在一定程度上讨论了其解的结构  相似文献   

9.
常见的离散Fourier变换(DFT)的推广均定义在一个交换环上。我们在[1]、[2]中给出了DFT在一类非交换环上的推广(FGFT),并将它应用于一些快速线性计算问题。本文将不加证明地列出这些快速算法的并行计算效率。结果表明,这些计算问题亦具有很好的并行性。  相似文献   

10.
李厚彪  钟尔杰 《计算数学》2015,37(4):401-414
本文研究了热传导方程初边值问题的半离散化差分格式直接解算法.分别从Dirichlet和Neumann边界条件出发,直接由空间差分格式导出与时间相关的一阶常微分方程组,随后通过正/余弦变换获得了原方程的半解析解,并给出了相关收敛性分析.并对中心差分格式和紧差分格式的精度差异,通过矩阵特征值理论给出了相关原因分析.另外,对于二维热传导方程初边值问题,应用矩阵张量积运算,该直接解算法可直接演变成二重正(余)弦变换.该方法由于不涉及时间上的离散,从而具有较好的计算效率.  相似文献   

11.
Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform (DCT) and the discrete Fourier transform (DFT) for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O(N) that are reduced greatly compared with O(N log N) by the classical trigonometric transforms.  相似文献   

12.
车牌定位技术是车牌识别技术中最重要的部分,利用车牌图像在DCT域的水平和竖直能量值对图像进行进一步二值化处理,通过中值滤波和小区去除定位车牌.实验结果表明这种车牌定位方法具有算法实现简单、速度快、适应性强的特点.  相似文献   

13.
We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.  相似文献   

14.
In this paper we propose the well-known Fourier method on some non-tensor productdomains in R~d, inclding simplex and so-called super-simplex which consists of (d 1)!simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallelhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended mostof concepts and results of the traditional Fourier methods on multivariate cases, such asFourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT)and related fast algorithms over a simplex. The relationship between the basic orthogonalsystem and eigen-functions of a Laplacian-like operator over these domains is explored.  相似文献   

15.
We suggest the two new discrete differential sine and cosine Fourier transforms of a complex vector which are based on solving by a finite difference scheme the inhomogeneous harmonic differential equations of the first order with complex coefficients and of the second order with real coefficients, respectively. In the basic version, the differential Fourier transforms require by several times less arithmetic operations as compared to the basic classicalmethod of discrete Fourier transform. In the differential sine Fourier transform, the matrix of the transformation is complex,with the real and imaginary entries being alternated, whereas in the cosine transform, the matrix is purely real. As in the classical case, both matrices can be converted into the matrices of cyclic convolution; thus all fast convolution algorithms including the Winograd and Rader algorithms can be applied to them. The differential Fourier transform method is compatible with the Good–Thomas algorithm of the fast Fourier transform and can potentially outperform all available methods of acceleration of the fast Fourier transform when combined with the fast convolution algorithms.  相似文献   

16.
Generalized Fourier transform on an arbitrary triangular domain   总被引:4,自引:0,他引:4  
In this paper, we construct generalized Fourier transform on an arbitrary triangular domain via barycentric coordinates and PDE approach. We start with a second-order elliptic differential operator for an arbitrary triangle which has the so-called generalized sine (TSin) and generalized cosine (TCos) systems as eigenfunctions. The orthogonality and completeness of the systems are then proved. Some essential convergence properties of the generalized Fourier series are discussed. Error estimates are obtained in Sobolev norms. Especially, the generalized Fourier transforms for some elementary polynomials and their convergence are investigated. This work was supported by the Major Basic Project of China (No. G19990328) and National Natural Science Foundation of China (No. 60173021).  相似文献   

17.
The main goal of this paper is to study about the continuous as well as discrete wavelet transform in terms of linear canonical Hankel transform (LCH‐transform) and discuss some of its basic properties. Parseval's relation and reconstruction formula of continuous linear canonical Hankel wavelet transform (CLCH‐wavelet transform) is obtained. Moreover, semidiscrete and discrete LCH‐wavelet transform are also discussed.  相似文献   

18.
Numerical Algorithms - In this paper, we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II that reconstructs the vector $\mathbf {x}\in \mathbb...  相似文献   

19.
A Fourier transform akin to Sneddon's R-transform is introduced. It is shown that the Hilbert transform links the two in much the same way as it connects the classical Fourier sine and cosine transforms.  相似文献   

20.
Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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