中心对称仿酉矩阵的构造及二元具有线性相位正交小波滤波器组的参数化

中心对称仿酉矩阵(简记为CSPM)在线性相位的小波滤波器组的构造中起着重要的作用,本文给出偶数阶CSPM的表达式,矩阵中的元素为二元一次多项式.基于已给出的CSPM,给出具有线性相位的二元正交小波滤波器组的参数化,通过选取不同的参数可以得到的具有线性相位的正交小波滤波器组.最后给出算例.     

基于仿酉矩阵的紧支撑二元正交小波滤波器组的构造

高维小波是处理多维信号的有力工具,张量积和栅格结构的小波有其自身的特点,但在实际应用中,我们仍需要构造小波滤波器来满足特定情形下的需要以提高滤波的效果,而构造正交滤波器,在多相域里就等价于构造仿酉阵,在本文中,我们通过对仿酉矩阵的研究,证明二元一次对称的仿酉阵一定能够块对角化,利用这种性质,给出了不可分离的二元正交小波滤波器组及线性相位小波滤波器的构造,并给出了相应的例子．     

仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

高维紧支撑正交对称的小波

基于仿酉矩阵的对称扩充方法,该文提出了一种尺度因子为3的紧支撑高维正交对称小波构造算法.即设φ(x)∈L~2(R~d)是尺度因子为3的紧支撑d维正交对称尺度函数,P(ξ)是它的两尺度符号,p_(0,v)(ξ)为P(ξ)的相位符号.首先提出一种向量的对称正交变换,应用对称正交变换对3~d维向量(p_(0,v)(ξ))_v,v∈E_d的分量进行对称化.通过仿酉矩阵的对称扩充,给出了3~d-1个紧支撑高维正交对称小波构造.这种方法构造的小波支撑不超过尺度函数的支撑.最后给出一个构造算例.     

中心对称仿酉矩阵的研究

我们通过对中心对称矩阵的讨论,给出了构造二元一次中心对称仿酉矩阵的充要条件,并给出了例子.     

正交多小波的构造

1 引言 在小波的构造和应用中,对于2尺度单一小波已有相当成熟的理论,特别是在小波构造方面,若知道正交单一尺度函数,相应的单一小波是很容易构造出的。对于a尺度紧支撑多小波,如何从已知的a尺度紧支撑多重尺度函数构造出相应的多小波,到目前为止尚没有一般的构造方法。W.Lanton等用仿酉矩阵扩充的方法构造出相应的多小     

a尺度正交的多小波

给出一种构造 a尺度正交多小波的方法 .它是由任意 a尺度正交的单小波及一组滤波器构造出来的 .由于 a尺度单正交尺度函数选取的任意性和滤波器的选取有相当大的自由度 ,使得有可能构造出大量 a尺度正交的多小波 .     

轮廓波变换原理及其构造方法

本文主要介绍轮廓波变换的基本原理,对轮廓波多方向性实现的关键技术——多维多采样率系统进行了阐述并详细说明了方向滤波器的构造过程,最后总结出了构造方向滤波器组常用的两种方法——McClellan变换法和多相位表示法,并给出了9×9参数化扇形滤波器组的构造实例.     

紧支撑的最小能量框架

基于仿酉矩阵扩充方法,本文构造了一维d带紧支撑的最小能量框架,给出了一维d带紧支撑最小能量框架的显式构造算法.所构造的最小能量框架的支撑不超过尺度函数的支撑.当所给的尺度函数具有对称性时,研究了紧支撑对称最小能量框架的结构.最后,构造了两个算例.     

α尺度r重正交共轭滤波器的构造

对于α尺度r重紧支撑正交多小波系统,给出了由长为L的α尺度r重正交共轭滤波器构造长为L+1的α尺度r重正交共轭滤波器的一般方法,也给出了由低阶矩阵滤波器构造高阶矩阵滤波器的方法.若给定的正交共轭滤波器满足完全重构条件,则利用算法构造新的滤波器也满足完全重构条件,算法还保持正交共轭滤波器对称性,这一点在信号处理方面具有很好的应用价值.     

Shift products and factorizations of wavelet matrices

A class of so-called shift products of wavelet matrices is introduced. These products are based on circulations of columns of orthogonal banded block circulant matrices arising in applications of discrete orthogonal wavelet transforms (or paraunitary multirate filter banks) or, equivalently, on augmentations of wavelet matrices by zero columns (shifts). A special case is no shift; a product which is closely related to the Pollen product is then obtained. Known decompositions using factors formed by two blocks are described and additional conditions such that uniqueness of the factorization is guaranteed are given. Next it is shown that when nonzero shifts are used, an arbitrary wavelet matrix can be factorized into a sequence of shift products of square orthogonal matrices. Such a factorization, as well as those mentioned earlier, can be used for the parameterization and construction of wavelet matrices, including the costruction from the first row. Moreover, it is also suitable for efficient implementations of discrete orthogonal wavelet transforms and paraunitary filter banks.and Cooperative Research Centre for Sensor Signal and Information ProcessingThis author is an Overseas Postgraduate Research Scholar supported by the Australian Government.     

Factorizations and construction of linear phase paraunitary filter banks and higher multiplicity wavelets

It is known that paraunitary matrices can be factorized into shift products of orthogonal matrices or linear factors. When the number of rows of such a matrix (i.e. the number of channels of a paraunitary filter bank) is even, the symmetry constraints corresponding to the linear phase property of the filter bank can be expressed as restrictions on factors — except the very first one, all must be centrosymmetric. For odd numbers of rows the situation is more complicated. It turns out that paraunitary matrices comprising an even number of square blocks do not exist and quadratic centrosymmetric factors have to be used in the 0-shift product factorization. The centrosymmetric linear and quadratic factors can be easily obtained from partitions of centrosymmetric orthogonal matrices. Their parameterizations are also described.The characterizations of paraunitary matrices obtained from these factorizations are complete; the question of the number of free parameters is discussed. Furthermore, the proposed factorizations also allow us to derive lattice structures for linear phase paraunitary filter banks and, since the basic regularity conditions can be incorporated as a constraint on the first factor, they can be used also for the construction of symmetric higher multiplicity wavelets.and Cooperative Research Centre for Sensor Signal and Information ProcessingThe author is an Overseas Postgraduate Research Scholar supported by the Australian Government.     

Parameterizations of Masks for Tight Affine Frames with Two Symmetric/Antisymmetric Generators

Parameterizations of FIR orthogonal systems are of fundamental importance to the design of filters with desired properties. By constructing paraunitary matrices, one can construct tight affine frames. In this paper we discuss parameterizations of paraunitary matrices which generate tight affine frames with two symmetric/antisymmetric generators (framelets). Based on the parameterizations, several symmetric/antisymmetric framelets are constructed.     

一类紧支撑矩阵值正交小波的构造

In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.     

向量值正交小波的构造与向量值小波包的特征

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed.A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory.An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented.Their characteristics is discussed by virtue of operator theory,time-frequency method.Moreover,it is shown how to design various orthonormal bases of space L2(R,Cn) from these wavelet packets.     

m-Band orthogonal vector-valued multiwavelets for vector-valued signals

In this paper, we introduce and study vector-valued multiresolution analysis with multiplicity r (VMRA) and m-band orthogonal vector-valued multiwavelets which have potential to form a convenient tool for analyzing vector-valued signals. Necessary conditions for orthonormality of vector-valued multiwavelets are presented in terms of filter banks. The existence of m-band vector-valued orthonormal multiwavelets is proved by means of bi-infinite matrix. The relationship between vector-valued multiwavelets and traditional multiwavelets are considered, and it is found that multiwavelets can be derived from row vector of vector-valued multiwavelets. The construction of vector-valued multiwavelets from several scalar-valued wavelets is proposed. Furthermore, we show how to construct vector-valued multiwavelets by using paraunitary multifilter bank, in particular, we give formulations of highpass filters when its corresponding lowpass filters satisfy certain conditions and m=2. An example is provided to illustrate this algorithm. At last, we present fast vector-valued multiwavelets transform in form of bi-infinite vector.     

A study on compactly supported orthogonal vector-valued wavelets and wavelet packets

In this paper, vector-valued multiresolution analysis and orthogonal vector-valued wavelets are introduced. The definition for orthogonal vector-valued wavelet packets is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is derived by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. The properties of the vector-valued wavelet packets are investigated by using operator theory and algebra theory. In particular, it is shown how to construct various orthonormal bases of L²(R, C^s) from the orthogonal vector-valued wavelet packets.