全通多相网络滤波器组的理论和设计

本文进一步研究了应用全通滤波器实现均匀N带滤波器组的设计理论。我们提出了一种两级全通型滤波器组的结构,第一级为周期性镜像半带滤波器,第二级为两个N/2带的带通滤波器组。第一级的阻带恰好可以抑制第二级的不可控带,实现了全通型多相滤波器的连续阻带持性。并且给出了综合滤波器组的实现方案,可以使整个分析/综合系统完全消除混叠和幅度失真。最后本文给出了一个实例。     

频域多通道UWB—SAR接收机结构分析

分析了一种基于频域多通道的超宽带合成孔径雷达(UWB-SAR)接收机结构。比较了各种滤波器原型在频域分割滤波器组中的性能，依据正交镜像滤波器组(QMF)原理，给出了一种切实可行的临界采样频域分割方法。     

分数阶傅里叶域两通道滤波器组

 基于两通道滤波器组构建的子带信号处理方法已在图像、语音信号处理中得到广泛的应用.本文从分数阶傅里叶域多抽样率信号处理基本理论和分数阶卷积定理出发,推导了分数阶傅里叶域两通道滤波器组准确重建的基本条件,并基于传统傅里叶域有限长标准正交镜像滤波器组和共轭正交镜像滤波器组的原型滤波器设计了分数阶傅里叶域标准正交镜像滤波器组和共轭正交镜像滤波器组.本文所提出的结论为分数阶傅里叶域滤波器组理论的建立提供了基本依据,同时也为分数阶傅里叶变换在图像、语音信号处理等工程实践中的应用奠定了理论基础.最后,仿真实验验证了所提分数阶傅里叶域滤波器设计方法的有效性.     

FIR完全重建滤波器组构造双正交小波基

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。     

一种可变带宽FRM滤波新结构

设计窄过渡带FIR滤波器的一种非常有效的方法是采用频率响应屏蔽技术(FRM).但是如果过渡带要求过窄,经典FRM滤波器各子滤波器的阶数会变得很高.据此,本文提出一种可变带宽镜像半带滤波FRM滤波新结构,通过增加两个镜像半带滤波器,将原型滤波器及其互补滤波器的镜像分别分成奇偶两部分,使得原型滤波器和屏蔽滤波器的设计更加灵活,并降低了滤波器的计算复杂度,达到了设计高效窄过渡带滤波器的目的.理论分析和实例均验证了该结构的有效性.     

广义镜像对称频率响应线性相位准正交滤波器组

本文研究了镜像对称频率响应特性的线性相位准正交滤波器组,新算法利于设计的快速收敛.信道数为偶数时,提出了一个广义线性乘积因子, 新的格型结构带有附加的自由变量参数,可用来提高滤波器的特性.信道数是奇数时,研究了新的结构因子,设计了奇数信道数的滤波器组.     

设计余弦调制QMF组的一种新方法

通过适当矩阵变换，本文首先将精确重建余弦调制正交镜像滤波器组的设计转化为一种带约束的非线性优化问题，它是一种带二次型约束的最小二乘（ＱＣＬＳ）优化问题，然后，我们提出了一种变参量的罚函数方法来有效求解该类ＱＣＬＳ优化问题，通过直接采用原型滤波器系数为优化变量，我们构造了一个特殊的凸函数作优化代价函数，故可获得该问题的全局最小点，最后，采用本文提出的设计方法进行了一个具体实例设计，结果表明我们的方法     

基于数字图像的子带编码的研究

子带编码(SBC)是图像编码中的一种有前途的编码方法。本文主要论述了图像的子带分解与重建原理，重点讨论了适合于子带编码的正交镜像滤波器组(QMF)的设计方法，包括一维与二维滤波器组，该成果很适合在ATM网络中应用。     

基于DSP+Builder线性相位滤波器组格型设计与实现

分析了线性相位完全重构滤波器组(LPPRF)的分析滤波器和综合滤波器,研究了一种线性相位滤波器组设计方法,格型结构。通过求解滤波器组的Lattice系数,进行了两通道线性相位完全重构滤波器组的格型结构设计。提出一种设计方案,利用DSP Builder技术,将Matlab/simulink设计工具和QuartusⅡ设计工具结合起来,实现有限冲激响应格型滤波器组.并以一个高阶低通FIR格型滤波器组的实现为例,设计并完成软硬件仿真与验证。结果表明,该方法简单易行,能满足设计要求。     

基于余弦调制滤波器组的一种高效实现

本文给出了基于余弦调制的ＦＩＲ分析／综合滤波器组的一种高铲实现结构，其分析节和综合节分别由多相结构和离散正余弦变换网络组成；去除了由ＤＦＴ网络的计算冗余，与文献」３「相比，有效减少了总的计算量，进一步提高计算效率，具有较大的理论意义和实用价值。计算机仿真结果证明了本实现结构。     

Digital filter bank design quadratic-constrained formulation

Formulate the filter bank design problem as an quadratic-constrained least-squares minimization problem. The solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters. The formulations of the perfect-reconstruction cosine-modulated filter bank, of the near-perfect-reconstruction pseudo-QMF bank, and of the two-channel biorthogonal linear-phase filter bank are derived using the proposed approach. Compared with other design methods, the proposed technique yields PR filter banks with much higher stopband attenuation. The proposed technique can also be extended to design multidimensional filter banks     

General design of nearly perfect polyphase filter banks

In a polyphase approach of filter banks with critical sampling, it is proposed to design and implement the elements of the synthesis section as approximations of the inverses of the elements in the analysis section. The conditions for such approximations to be valid are stated and a design procedure is described, along with the corresponding structure. The approach generalises theqmf method by adding more flexibility, since it relaxes the constraints on the analysis prototype filter specification and allows different complexities in both sections. The general approach can yield de-signs able to compete favourably withqmf and pseudo-QMF in many aspects.     

Time-varying analysis-synthesis systems based on filter banks andpost filtering

Perfect reconstruction (PR) time-varying analysis-synthesis filter banks are those in which the filters are allowed to change from one set of PR filter banks to another as the input signal is being processed. Such systems have the property that, in the absence of coding, they faithfully reconstruct every sample of the input. Various methods have been reported for the time-varying filter bank design; all of them, however, utilize structures for conventional PR filter banks. These conventional structures that have been applied in the past result in different limitations in each method. This paper introduces a new structure for exactly reconstructing time-varying analysis-synthesis filter banks. This structure consists of the conventional filter bank followed by a time-varying post filter. The new method requires neither the redesign of the analysis sections nor the use of any intermediate analysis filters during transition periods. It provides a simple and elegant procedure for designing time-varying filter banks without the disadvantages of the previous methods     

Discrete Lagrangian Methods for Designing Multiplierless Two-Channel PR-LP Filter Banks

In this paper, we present a new search method based on the theory of discrete Lagrange multipliers for designing multiplierless PR (perfect reconstruction) LP (linear phase) filter banks. To satisfy the PR constraints, we choose a lattice structure that, under certain conditions, can guarantee the resulting two filters to be a PR pair. Unlike the design of multiplierless QMF filter banks that represents filter coefficients directly using PO2 (powers-of-two) form (also called Canonical Signed Digit or CSD representation), we use PO2 forms to represent the parameters associated with the lattice structure. By representing these parameters as sums or differences of powers of two, multiplications can be carried out as additions, subtractions, and shifts. Using the lattice representation, we decompose the design problem into a sequence of four subproblems. The first two subproblems find a good starting point with continuous parameters using a single-objective, multi-constraint formulation. The last two subproblems first transform the continuous solution found by the second subproblem into a PO2 form, then search for a design in a mixed-integer space. We propose a new search method based on the theory of discrete Lagrange multipliers for finding good designs, and study methods to improve its convergence speed by adjusting dynamically the relative weights between the objective and the Lagrangian part. We show that our method can find good designs using at most four terms in PO2 form in each lattice parameter. Our approach is unique because our results are the first successful designs of multiplierless PR-LP filter banks. It is general because it is applicable to the design of other types of multiplierless filter banks.     

Eigenfilter Approach to the Design of One-Dimensional and Multidimensional Two-Channel Linear-Phase FIR Perfect Reconstruction Filter Banks

We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a “predesigned” analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.      

基于加权总体最小二乘正则化方法的混合滤波器组最优化设计

模拟分析滤波器组的实现欠理想、系统噪声以及数字综合滤波器有效阶数实现所带来的系统误差均有可能造成混合滤波器组的设计出现解不稳定、无唯一解等病态问题,影响混合滤波器组的准确重构效果。本文首先给出了满足准确重构条件下,以综合滤波器组频域响应为求解变量的混合滤波器组线性求解模型。针对线性方程中系数矩阵以及目标向量受扰动误差影响特点,提出一种新的基于加权总体最小二乘正则化算法的IIR形式综合滤波器设计方法。算法以系统扰动误差最小化为目标函数,根据随机误差变量的二阶统计特性,采用加权总体最小二乘算法抑制滤波器实现误差以及随机噪声等扰动因素影响,使得到的综合滤波器组频域响应解的加权误差平方和最小化,并通过Tikhonov正则化方法优化病态情况下方程组解的稳定性。提出一种IIR类型的综合滤波器系数的求解算法,并利用正则化方法优化滤波器系数,提高系统稳定性。该方法可应用于过采样混合滤波器组的设计。仿真结果表明该算法的有效提高系统鲁棒性和改善重构性能。      

Near-perfect-reconstruction pseudo-QMF banks

A novel approach to the design of M-channel pseudo-quadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is constrained to be a linear-phase spectral-factor of a 2Mth band filter. As a result, the overall transfer function of the analysis/synthesis system is a delay. Moreover, the aliasing cancellation (AC) constraint is derived such that all the significant aliasing terms are canceled. Consequently, the aliasing level at the output is comparable to the stopband attenuation of the prototype filter. In other words, the only error at the output of the analysis/synthesis system is the aliasing error which is at the level of stopband attenuation. Using this approach, it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of -100 dB. Moreover, the resulting reconstruction error is also on the order of -100 dB. Several examples are included     

无约束法设计完全重构M带滤波器组

本文提出了一种新的正交和双正交完全重构M带滤波器组的设计方法.这种方法是建立在多项式分解基础之上,可在无约束条件下设计,所设计的滤波器组具有结构化完全重构特点,对于双正交滤波器组还可以方便设计系统时延.和已有的方法相比,新方法具有低设计复杂度特点.文中还描述了设计过程,最后给出了设计例子和结果.     

基于二进小波变换的实信号的多尺度Hilbert变换和瞬时频率提取

该文着重讨论了使用二进小波变换方法实现数字Hilbert滤波,特别是使用滤波器组实现多尺度Hilbert滤波所要考虑的各尺度滤波器的设计问题。将多尺度Hilbert方法应用到求信号的瞬时参数中,并利用小波变换的去噪思想,取得了比使用DWT方法去噪更好的去噪效果。     

Analysis, design, and implementation of two-channel linear-phasefilter banks: a new approach

The problem of designing two-channel perfect-reconstruction FIR filter banks with linear-phase analysis and synthesis filters is revisited. Based on a new algebraic formulation, all the possible factorized forms for this two-band filter bank are derived. We thus obtain complete and canonical solutions for the filter banks, composed of odd-order symmetric and antisymmetric filters (type-A systems) and for those built with symmetric even order filters (type-B systems). A strong characteristic of these new cascade structures, which, until now, had not been identified, is related to a defectivity property. Taking this into account is the key issue to cover all the FIR solutions and to design cascade structures being robust to the quantization of their parameters. Design examples are provided that illustrate our method