具有对称或反对称滤波器组的双正交平衡多小波

通过对待定矩阵滤波器组的定义,构造了具有对称性,平衡性和高阶消失矩的双正交多小波.它的滤波器组具有有利于实际应用的对称性,其结构类似于标量小波,即可以用两支滤波器确定,所构造的多小波无疑是一类新型的多小波.     

紧支撑正交多小波的构造

通过选取初等旋转矩阵和初等反射矩阵,利用多分辨分析以及矩阵理论,给出了一种由已知紧支撑对称正交多小波构造具有相应性质多小波的方法.利用该方法还可以构造出一类平衡小波.最后,结合DGHM紧支撑对称正交多小波给出了具体的算例.     

双正交多小波滤波器构建

阐述了由Charles A Micchelli,Yuesheng Xu建立的基于不变集的多小波理论,以此为基础讨论了有着自仿映射区间特性的双正交多小波的滤波器构建.     

小波滤波器组

讨论了正交滤波器组和斜交滤波器组,以及它们之间的关系,小波的构造是小波分析中的根本问题。而在小波的构造中,滤波器组起着重要的作用。紧支集正交小波、样条小波和双正交小波等都是利用滤波器组来构造的。这些讨论在小波构造中是非常有用的。     

二重紧支撑对称—反对称多小波的构造

在给定的一个紧支撑正交单小波基础上,将其平移做为多个小波函数来构造二重紧支撑对称多小波,再选取合适的正交矩阵与所构造的二重紧支撑对称多小波做乘积,进而构造相应性质的二重紧支撑对称-反对称多小波.以提升Haar小波为例给出了具体的构造过程.应用这种方法构造对称-反对称多小波将极其容易.     

双正交紧支集小波因果滤波器组

证明了双正交紧支集小波可构成准确重构系统,给出双正交紧支集小波因果滤波器组构成准确重构系统的条件及滤波器组中各滤波器的冲激响应,为滤波器的物理实现奠定了基础。     

伸缩因子为M的FIR正交向量滤波器组的特征

讨论伸缩因子为M(大于2)的有限脉冲响应正交滤波器组的分解形式，同时给出了正交有限脉冲响应滤波器组的构造方法。     

对称-反对称正交多小波及其相关的单小波

本文指出对称-反对称正交多小波和与它相关的长度为4N的单小波之间的关系.介绍两种利用低通矩阵序列来构造高通矩阵序列的方法,并利用这两种方法给出两种通过单小波来构造对称-反对称正交多小波的方法.     

对称平衡多小波的设计

平衡多小波由于可避免预滤波而成为小波分析的研究热点。对已有不平衡多小波进行平衡,常会丢失多重尺度函数的对称性。通过对多小波进行平衡时多尺度函数保留对称性的充要条件进行研究,导出了具对称多重尺度函数的平衡多小波的构造算法,给出了2重对称平衡多小波的滤波器系数。     

具有某种对称性质的正交多小波构造

当把尺度函数的滤波带看作标量滤波，其每一行具有对称、反对称性质时，能够构造具有类似性质的正交多小波．这里讨论的对称、反对称性质是不同于尺度函数和多小波的对称、反对称性质，此时尺度函数和多小波是不具有对称和反对称性质的．这里，仅考虑重数是3，同时矩阵滤波的长度是奇数的情况．     

A class of compactly supported symmetric/antisymmetric B-spline wavelets

An algorithm for constructing a class of compactly supported symmetric/antisymmetric B-spline wavelets is presented.For any m th order and k th order cardinal B-spline Nm (x), Nk (x), if m k is an even integer, the corresponding m th order B-spline wavelets ψkm (x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψkm (x), m ＞ 1 is m th Bspline wavelet associated with two spline functions Nm (x) and Nk (x), then (ψkm (x))′( x ) is m - 1th B-spline wavelet associated with Nm-1(x) and Nk 1(x), i.e. (ψkm(x))′(x) =22ψk 1m-1(x). Similarly, ∫x0 ψkm(t)dt, k ＞1 is m 1th B-spline wavelet associated with Nm 1 (x) and Nk-1 (x). Using this method, we recovered Chui and Wang' s spline wavelets. Since a class of B-spline wavelets are symmetric/antisymmetric, their linear phase property is assured. Several examples are also presented.     

基于M带滤波器组的视频编码方法

提出了一种基于M带滤波器组的视频编码方法，应用一种新的格型结构，用较少的参数设计M带滤波器组，同时引入正则性指标，针对正交和双正交系统分析提出了不同的参数化方法，在此基础上,提出了本文的视频编码方案中，应用设计出的滤波器组系数做变换，对零树编码采用显式量化和零树先深算法，快速有效地生成零树，与H．263相比，其性能有较大幅度的提高。     

Some properties on multivariate filter banks with a matrix factorization

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.     

Design of perfect reconstruction rational sampling filter banks

The design of rational sampling filter banks based on a recombination structure can be formulated as a problem with two objective functions to be optimized. A new hybrid optimization method for designing perfectreconstruction rational sampling filter banks is presented, which can be used to solve a class of problems with two objective functions. This method is of good convergence and mezzo calculation cost. Satisfactory results free of aliasing in analysis and synthesis filters can be obtained by the proposed method.     

FMT系统中滤波器组的优化设计

基于滤波多音频（FMT）技术,给出了系统中滤波器组的设计,针对系统的某些特定要求对滤波器组的设计方法进行了优化,并对优化前后的系统在无线信道中的性能进行了仿真实验比较,结果表明,滤波器组的优化设计改善了系统的性能。     

音频编码中非均匀滤波器组的构造

为了更好地满足音频编码中时频映射的技术要求,基于频变调制重叠变换(FV-MLT),推导出更具一般性的频变扩展重叠变换(FV-ELT),从而构造了一类具有可变时频分辨率特性的滤波器组。它既可为瞬态音频信号提供灵活的时频映射,又保证稳态信号时有很高的频率分辨率。理论分析结果表明FV-ELT比MLT和FV-MLT有更高的变换增益,以8子带为例的仿真结果,也进一步验证FV-ELT提供了更好的时频分析特性。因此FV-ELT是非常适于音频编码时频分析的一类滤波器组,能够有效提高编码效率。     

Analysis of realizable rational decimated nonuniform filter banks with direct structure

In the design of nonuniform filter banks （NUFBs） with direct structure, the location of each analysis filter, corresponding to the sampling factor satisfying maximal decimation condition, should be set properly to avoid large aliasing. In this paper, a necessary and sufficient condition for the setting of the location of each analysis filter is derived. The NUFBs, we focus on, have rational decimation factors. Based on the derived condition, the frequency support of each analysis filter for the realizable NUFBs can be determined directly in such a way that the analysis filters can extract the corresponding bands of the input signal. This provides a guideline for the design of NUFBs with direct structure in choosing proper locations of analysis filters.     

Fusion of multispectral and panchromatic images using multirate filter banks

In this paper, an image fusion method based on the filter banks is proposed for merging a high-resolution panchromatic image and a low-resolution multispectral image. Firstly, the filter banks are designed to merge different signals with minimum distortion by using cosine modulation. Then, the filter banks-based image fusion is adopted to obtain a high-resolution multispectral image that combines the spectral characteristic of low-resolution data with the spatial resolution of the panchromatic image. Finally, two different experiments and corresponding performance analysis are presented. Experimental results indicate that the proposed approach outperforms the HIS transform, discrete wavelet transform and discrete wavelet frame.