共查询到20条相似文献,搜索用时 93 毫秒
1.
定义了二维Haar尺度函数,构造了长方形区域上的二维非均匀Haar小波函数,给出了非均匀 Haar 小波的分解和重构公式,最后得到了单值重构算法. 相似文献
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我们提出了最优多进Haar小波的概念,证明了其存在性和唯一性,给出了最优多进Haar小波构造的通用方法,并证明了最优多进Haar小波具有线性相位,在消失矩意义下,我们所得到的最优多进Haar小波优于离散余弦变换.同时,我们用图像缩编码的方法验证了最优多进Haar小波的性能优于离散余弦变换的,新的变换可以化为精确的小整数运算,能非常廉价地用集成电路实现,该变换的实用意义在于给图像和视频压缩提供了一个更好的选择. 相似文献
3.
《数学的实践与认识》2020,(1)
借助Haar小波正交函数的分数阶积分算子矩阵,通过离散未知变量,将待求Poisson方程转化为大型的线性代数方程组,然后利用Matlab软件进行编程求解,即可求得原问题的未知系数矩阵,代入原方程,从而求得数值解.数值结果表明,当Haar小波采取很小的级数项展开时,即可获得满意的数值精度,而且算法比较稳定,有很强的实际应用价值. 相似文献
5.
三角域上一类正交函数系的构造 总被引:3,自引:0,他引:3
V系统是作者2005年构造的一类L2[0,1]空间上的正交完备函数系. κ次V系统由κ次分片多项式组成,具有多分辨特性,是Haar小波函数的推广.基于V系统的正交表达,可以对CAGD中常见的几何模型用有限项V-级数做到精确重构,完全消除Gibbs现象,这是有限项Fourier级数或连续小波级数不能做到的.针对多变量情形,给出了三角域上的κ次正交V系统的构造方法.三角域上的V系统的重要应用显现在对3D复杂几何图组的整体频谱分析上. 相似文献
6.
(五 )离散小波变换正交小波基上面我们介绍了连续小波变换 ,但在实际问题及数值计算中更重要的是其离散形式 (在作具体数值计算时 ,连续小波的参数 a,b必然要离散化 )。对确定的小波母函数ψ( t) ,取定 a0 >1 ,b0 >0 令ψmn( t) =am20 ψ( am0 t-nb0 ) , m,n∈ Z ( 5.1 )这里 Z表示全体整数所构成的集合 ,我们称 ψmn( t)为离散小波。对于函数 f( t) ,相应的离散小波变换为 :Cf( m,n) =∫∞-∞f ( t)ψmn( t) dt,m,n∈ Z ( 5.2 ) 我们知道对连续小波 ,由 Wf( a,b) ,a,b∈ ( -∞ ,∞ ) ,a≠ 0可唯一确定函数 f ( t) (反演公式( 3 .… 相似文献
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尽管小波分析已取得了许多重要成就,但主要集中在函数空间内.例如,不确定性原理的研究就是这样.然而,从应用的角度看(从图像压缩到数值计算),研究离散空间中的小波更加自然,更为重要.因此将研究离散空间l2(ZN)中的不确定性原理,D4类小波以及其它一些小波的时频局部性质. 相似文献
11.
斜变换ST的演化生成与快速算法 总被引:9,自引:0,他引:9
1.引言 含有“斜”基向量的正交变换(斜变换 ST)概念是由 Enomoto & Shibata(1971)提出的[1].斜向量是一个在其范围内呈均匀阶梯下降的离散锯齿波形.对于亮度逐渐改变的图象,用斜向量来表示是适合的. Enomoto & Shibata仅考虑了斜向量长度为 4和 8的情况.Pratt等人利用递推性将 ST推广到 N= 2m阶的情形,给出了 ST的一般定义[2],并与其它变换进行了比较[3].ST已成功地用在图象编码上,而且在非正弦类交换编码的应用中,斜变换的效果最好[2,3]. Ah… 相似文献
12.
V. G. Gasenko 《Journal of Applied and Industrial Mathematics》2017,11(1):40-48
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
13.
关于一类非连续的正交函数及其应用的探讨 总被引:4,自引:0,他引:4
齐东旭 《高校应用数学学报(A辑)》1990,5(1):39-46
本文研究一类新的非连续分段线性函数系,它是正交且完备的。特别讨论了它与离散斜变换的内在联系,从而建立直接的快速算法。分析表明这些结果有希望作为数字信号处理某些问题的新的有效的数学工具。 相似文献
14.
Manfred Tasche 《Numerical Algorithms》1993,5(9):453-464
Applying orthogonal polynomials, the discrete Chebyshev-Vandermonde transform (DCVT) is introduced as a special almost orthogonal transform. An important example of DCVT is the discrete cosine transform (DCT). Using the divide-and-conquer technique and the d'Alembert functional equation, fast DCT-algorithms are described. By the help of these results we present for the first time fast, numerically stable algorithms for simultaneous polynomial approximation and for collocation method for the airfoil equation, a special Cauchytype singular integral equation. 相似文献
15.
David K. Maslen 《Journal of Fourier Analysis and Applications》1998,4(1):19-52
This article genralizes the fast Fourier transform algorithm to the computation of Fourier transforms on compact Lie groups.
The basic technique uses factorization of group elements and Gel'fand-Tsetlin bases to simplify the computations, and may
be extended to treat the computation of Fourier transforms of finitely supported distributions on the group. Similar transforms
may be defined on homogeneous spaces; in that case we show how special function properties of spherical functions lead to
more efficient algorithms. These results may all be viewed as generalizations of the fast Fourier transform algorithms on
the circle, and of recent results about Fourier transforms on finite groups.
Acknowledgements and Notes. This paper was written while the author was supported by the Max-Planck-Institut für Mathematik, Bonn, Germany. 相似文献
16.
Katja Ihsberner 《Numerical Algorithms》2007,46(1):1-22
Discrete cosine transforms (DCT) are essential tools in numerical analysis and digital signal processing. Processors in digital
signal processing often use fixed point arithmetic. In this paper, we consider the numerical stability of fast DCT algorithms
in fixed point arithmetic. The fast DCT algorithms are based on known factorizations of the corresponding cosine matrices
into products of sparse, orthogonal matrices of simple structure. These algorithms are completely recursive, are easy to implement
and use only permutations, scaling, butterfly operations, and plane rotations/rotation-reflections. In comparison with other
fast DCT algorithms, these algorithms have low arithmetic costs. Using von Neumann–Goldstine’s model of fixed point arithmetic,
we present a detailed roundoff error analysis for fast DCT algorithms in fixed point arithmetic. Numerical tests demonstrate
the performance of our results.
相似文献
17.
Jiachang Sun 《计算数学(英文版)》2006,24(3):305-322
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
18.
Hong-xia Wang Li-zhi Cheng 《应用数学学报(英文版)》2005,21(3):459-468
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
19.
The representation theory of Abelian groups is used to obtain an algebraic divide-and-conquer algorithm for computing the finite Fourier transform. The algorithm computes the Fourier transform of a finite Abelian group in terms of the Fourier transforms of an arbitrary subgroup and its quotient. From this algebraic algorithm a procedure is derived for obtaining concrete factorizations of the Fourier transform matrix in terms of smaller Fourier transform matrices, diagonal multiplications, and permutations. For cyclic groups this gives as special cases the Cooley–Tukey and Good–Thomas algorithms. For groups with several generators, the procedure gives a variety of multidimensional Cooley–Tukey type algorithms. This method of designing multidimensional fast Fourier transform algorithms gives different data flow patterns from the standard “row–column” approaches. We present some experimental evidence that suggests that in hierarchical memory environments these data flows are more efficient. 相似文献
20.
Computation of the fractional Fourier transform 总被引:1,自引:0,他引:1
Adhemar Bultheel Hctor E. Martínez Sulbaran 《Applied and Computational Harmonic Analysis》2004,16(3):182-202
In this paper we make a critical comparison of some
programs for the digital computation of the fractional Fourier transform that are freely available and we describe our own implementation that filters the best out of the existing ones. Two types of transforms are considered: first, the fast approximate fractional Fourier transform algorithm for which two algorithms are available. The method is described in [H.M. Ozaktas, M.A. Kutay, G. Bozda
i, IEEE Trans. Signal Process. 44 (1996) 2141–2150]. There are two implementations: one is written by A.M. Kutay, the other is part of package written by J. O'Neill. Second, the discrete fractional Fourier transform algorithm described in the master thesis by Ç. Candan [Bilkent University, 1998] and an algorithm described by S.C. Pei, M.H. Yeh, and C.C. Tseng [IEEE Trans. Signal Process. 47 (1999) 1335–1348]. 相似文献