共查询到19条相似文献,搜索用时 250 毫秒
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给出了一种利用B样条构造具有线性相位的紧支集对偶尺度函数,对应的紧支集双正交小波及其相应的FIR滤波器组的方法。 相似文献
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一种基于正交多小波的自适应均衡算法 总被引:1,自引:0,他引:1
该文提出了用正交多小波来表示均衡器,由于多小波可同时具有正交性、紧支性和线性相位等特点,因此经多小波变换后所得到的信号相关阵的稀疏化估计与单小波变换相比非零元素较少,边界效应减小,基于此,文中给出了正交多小波变换域的一种Newton-LMS类自适应均衡算法,其计算复杂性可通过有预处理的共轭梯度法进一步降低为O(N log N),仿真结果表明了该算法收敛速度较快,且易于实时实现。 相似文献
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给出一种由正交多尺度函数构造其相应正交多小波的新方法,该方法具有计算简单且不受多小波重数限制的特点,不用求解关于多元未知矩阵的非线性方程组或进行相应的多项式矩阵的因子分解。与已有的通过选取参数来确定多小波系统的方法相比,因为他由尺度序列直接确定小波序列,不必考虑改变参数时这两个序列之间相关的变化,所以更便于灵活地设计出具有各种所需特性的多小波系统。用该方法重新导出了GHM多小波。 相似文献
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本文论述了由双正交完全重建滤波器组构造高度正则的双正交小波基的充分条件和构造方法,系统地研究了双正交线性相位FIR完全重建滤波器组的解的结构和已知H0(z)构造完全重建滤波器组的方法,并且实现了用单一的传递函数A(z)构造线性相位FIR双正交完全重建滤波器组的设计方法。这种方法的突出优点是滤波器组分析、合成部分中的滤波器可以用数值优化的方法使两者同时逼近理想低通滤波器和理想高通滤波器,即具有良好的频率选择性,并且所有滤波器都具有线性相位的特点。该滤波器组具有良好的梯形实现结构。在具体的滤波器设计中提出了基于均方误差最小准则的特征滤波器的设计方法和基于误差最大值最小准则的Remez交换法。而且上述方法设计的滤波器组可以构造出具有高度正则性的光滑的双正交小波基。 相似文献
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为设计线性完全重构的二维滤波器组,引用了计算代数中的Groebner基方法,根据线性相位条件和完全重构条件,分别设计出二维滤波器组的分析滤波器和综合滤波器的多相元矩阵,给出其参数化形式。根据小波构造理论,利用所设计的分析滤波器组构造出一个对称的纯二维小波。设计结果显示了Groebner基方法的有效性,设计方法更为简单。 相似文献
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为了提高复小波变换的效率,本文提出了一种设计Q-shift复小波滤波器的新方法。与目前采用多相位矩阵的晶格分解结构得到正交小波的方法不同的是,这里从更为一般的完全重构滤波器组出发寻求满足特定要求的正交小波。不但可以构造出系数更为简单、运算更加方便的小波,而且可以实现任意精度的复小波变换。该方法的可拓展性好,可以很方便的添加如高阶消失矩等限制并简化设计过程。以普遍采用的Q-shift10/10小波为例,利用本文构造的正交小波可将复小波变换中的乘法运算降低到原来的1/3,而加法基本相当,且小波的频率选择性质更好。将其用于图像去噪的实验表明,采用本文构造的小波可以显著提高处理速度并得到更高的峰值信噪比(PSNR)。 相似文献
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With the exception of the Haar basis, real-valued orthogonal wavelet filter banks with compact support lack symmetry and therefore do not possess linear phase. This has led to the use of biorthogonal filters for coding of images and other multidimensional data. There are, however, complex solutions permitting the construction of compactly supported, orthogonal linear phase QMF filter banks. By explicitly seeking solutions in which the imaginary part of the filter coefficients is small enough to be approximated to zero, real symmetric filters can be obtained that achieve excellent compression performance 相似文献
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Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of order-factorable wavelets imposes a simple constraint on each of its polynomial order-1 factors. We thus obtain a simple and complete method of constructing orthogonal order-factorable wavelets with linear phase. This method is exemplified by design in the case of four-band separable sampling. An interesting result that is similar to the one well-known in the one-dimensional (1-D) case is obtained: orthogonal order-factorable wavelets cannot be both continuous and have four-fold symmetry 相似文献
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Xiao-Ping Zhang Desai M.D. Ying-Ning Peng 《Signal Processing, IEEE Transactions on》1999,47(4):1039-1048
Previous wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In this paper, we prove that a linear-phase complex orthogonal wavelet does not exist. We study the implications of symmetry and linear phase for both complex and real-valued orthogonal wavelet bases. As a byproduct, we propose a method to obtain a complex orthogonal wavelet basis having the symmetry property and approximately linear phase. The numerical analysis of the phase response of various complex and real Daubechies wavelets is given. Both real and complex-symmetric orthogonal wavelet can only have symmetric amplitude spectra. It is often desired to have asymmetric amplitude spectra for processing general complex signals. Therefore, we propose a method to design general complex orthogonal perfect reconstruct filter banks (PRFBs) by a parameterization scheme. Design examples are given. It is shown that the amplitude spectra of the general complex conjugate quadrature filters (CQFs) can be asymmetric with respect the zero frequency. This method can be used to choose optimal complex orthogonal wavelet basis for processing complex signals such as in radar and sonar 相似文献
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Wavelets with convolution-type orthogonality conditions 总被引:5,自引:0,他引:5
Wavelets with free parameters are constructed using a convolution-type orthogonality condition. First, finer and coarser scaling function spaces are introduced with the help of a two-scale relation for scaling functions. An inner product and a norm having convolution parameters are defined in the finer scaling function space, which becomes a Hilbert space as a result. The finer scaling function space can be decomposed into the coarser one and its orthogonal complement. A wavelet function is constructed as a mother function whose shifted functions form an orthonormal basis in the complement space. Such wavelet functions contain the Daubechies' compactly supported wavelets as a special case. In some restricted cases, several symmetric and almost compactly supported wavelets are constructed analytically by tuning free convolution parameters contained in the wavelet functions 相似文献
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Tai-Chiu Hsung Lun D.P.-K. Yu-Hing Shum Ho K.C. 《Signal Processing, IEEE Transactions on》2007,55(12):5619-5629
Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the prefilter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. 相似文献
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A unified approach for constructing a large class of multiwavelets is presented. This class includes Geronimo-Hardin-Massopust (1994), Alpert (1993), finite element and Daubechies-like multiwavelets. The approach is based on the characterisation of approximation order of r multiscaling functions using a known compactly supported refinable super-function. The characterisation is formulated as a generalised eigenvalue equation. The generalised left eigenvectors of the finite down-sampled convolution matrix L/sub f/ give the coefficients in the finite linear combination of multiscaling functions that produce the desired super-function. The unified approach based on the super-function theory can be used to construct new multiwavelets with short support, high approximation order and symmetry. 相似文献