基于进行计算设计无法的完全重构两通道滤波器组

该文提出了一种设计无乘法完全重构的两通道滤波器组的方法。这种滤波器组在基于对提升模式结构改进的研究成果之上,提出了给定初始值的进化计算搜索设计方法。这种设计方法具有比用遗传算法快的特点。文中详细描述了此算法的过程,并给出了设计例子和结果。     

基于遗传算法的两通道完全重构滤波器组的设计

介绍了两通道滤波器组的完全重构条件,利用Euclidean分解算法,将两通道滤波器组的设计问题简化为寻找给定特性的低通滤波器的最佳Euclidean互补滤波器的单变量非线性优化问题,并探讨了采用遗传算法设计此类高度非线性优化问题.最后通过设计例子说明将遗传算法应用到滤波器组的设计中是可行的.     

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.     

两通道低延迟滤波器组的设计

本文提出了一种用有效的迭代拉格朗日乘子法设计精确重构的两通道低延迟滤波器组.该方法具有较高的计算效率,既能设计不同长度也能设计相同长度的滤波器组.文中给出了设计例子并与其它方法进行了比较.结果表明,用该方法设计的两通道低延迟滤波器组具有更高的阻带衰减.     

临界采样余弦调制滤波器组算法综述

在多速率数字信号处理系统中,余弦调制滤波器组受到广泛关注.它是一种常用的滤波器组,可以通过对低通原型滤波器优化并进行余弦调制得到分析和综合滤波器组,并且可以做到对信号的完全重构,具有计算复杂度低和设计简单等优点.该文综述了余弦调制滤波器组的发展过程及各种算法.     

基于提升方法的滤波器组因子分解

讨论了FIR滤波器组的分解.2通道完全重构FIR 子波变换分解可为有限步的提升步骤,使用Laurent多项式的辗转相除法给出了这种分解的一个代数方法的证明;证明了二通道子波变换的分解定理不能平行推广到2M通道滤波器组.提出使用M-通道滤波器组构造2M-通道滤波器组,它由多相矩阵的分块化和提升方法实现,这种方法易于构造非线性滤波器组,如整数变换.     

两通道完全重构滤波器组的设计方法:因式分解法

本文首先研究了两通道滤波器组设计的完全重构的条件以及Euclidean多项式的性质,提出了基于因式分解的两通道完全重构滤波器组的设计方法.该方法不需要进行强的非线性优化计算而可以实现真正的结构化的完全重构滤波器组.文中描述了这种方法的推导过程,给出了设计步骤,最后通过给出的设计例子,说明该方法是有效的.     

两通道完全重构滤波器组的设计方法:因式分解法

本文首先研究了两通道滤波器组设计的完全重构的条件以及Euclidean多项式的性质 ,提出了基于因式分解的两通道完全重构滤波器组的设计方法 .该方法不需要进行强的非线性优化计算而可以实现真正的结构化的完全重构滤波器组 .文中描述了这种方法的推导过程 ,给出了设计步骤 ,最后通过给出的设计例子 ,说明该方法是有效的     

基于自适应优化的经验数据分解滤波器的设计

对经验数据分解算法进行了研究,从滤波器完全重构出发,研究了经验数据分解滤波器与两通道滤波器组对应滤波器参数的关系,得出分析和综合滤波器都为FIR滤波器应满足的条件.可根据不同的应用对分析高通滤波器进行灵活地设计,并保证重建滤波器是FIR滤波器.利用离散线性定常系统的最优滤波和预测技术对分析高通滤波器的系数进行了预测,使用超光谱图像数据进行测试分析,确定了最佳预测滤波器的系数.结合JPEG2000的核心算法EBCOT对超光谱图像数据进行处理,并比较了该算法的输出码率同JPEG2000中无损压缩输出码率.结果表明经验数据分解算法产生的图像输出码率比JPEG2000中无损压缩输出码率平均小0.217bpp,是一种对非平稳数据有效的分析方法.     

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。     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Theory of paraunitary filter banks over fields of characteristictwo

Motivated by our wavelet framework for error-control coding, we proceed to develop an important family of wavelet transforms over finite fields. Paraunitary (PU) filter banks that are realizations of orthogonal wavelets by multirate filters are an important subclass of perfect reconstruction (PR) filter banks. A parameterization of PU filter banks that covers all possible PU systems is very desirable in error-control coding because it provides a framework for optimizing the free parameters to maximize coding performance. This paper undertakes the problem of classifying all PU matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary PU building blocks and a factorization technique that is specialized to obtain a complete realization for all PU filter banks over fields of characteristic two. This is proved for the 2 × 2 case, and conjectured for the M × M case, where M ⩾ 3. Using these elementary building blocks, we can construct all PU filter banks over fields of characteristic two. These filter banks can be used to implement transforms which, in turn, provide a powerful new perspective on the problems of constructing and decoding arbitrary-rate error-correcting codes     

Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.     

Synthesis of extremal wavelet-generating filters using Gaussianquadrature

Orthogonal wavelets can be generated from finite impulse response quadrature mirror filters; these filters are also used in perfect reconstruction filter banks. This paper addresses the problem of efficiently synthesizing such filters. A class of extremal filters is defined by the property that their magnitude spectrum maximizes an integral criterion. It is found that these filters are characterized by their zeros on the unit circle, which frequently can be obtained from a set of orthogonal polynomials. A family of filters is constructed that minimize the subband aliasing energy and can generate wavelets with an arbitrary number of vanishing moments. The algorithm for generating these filters makes use of the Levinson recursions, Gaussian quadrature and a fast version of Euclid's algorithm. Similar to other methods for constructing quadrature mirror filters, the spectral factorization of a polynomial is the computationally expensive part of this algorithm     

Construction of Two-Dimensional Paraunitary Filter Banks Over Fields of Characteristic Two and Their Connections to Error-Control Coding

Filter banks over finite fields have found applications in digital signal processing and error-control coding. One method to design a filter bank is to factor its polyphase matrix into the product of elementary building blocks that are fully parameterized. It has been shown that this factorization is always possible for one-dimensional (1-D) paraunitary filter banks. In this paper, we focus on two-channel two-dimensional (2-D) paraunitary filter banks that are defined over fields of characteristic two. We generalize the 1-D factorization method to this case. Our approach is based on representing a bivariate finite-impulse-response paraunitary matrix as a polynomial in one variable whose coefficients are matrices over the ring of polynomials in the other variable. To perform the factorization, we extend the definition of paraunitariness to the ring of polynomials. We also define two new building blocks in the ring setting. Using these elementary building blocks, we can construct FIR two-channel 2-D paraunitary filter banks over fields of characteristic two. We also present the connection between these 2-D filter banks and 2-D error-correcting codes. We use the synthesis bank of a 2-D filter bank over the finite field to design 2-D lattice-cyclic codes that are able to correct rectangular erasure bursts. The analysis bank of the corresponding 2-D filter bank is used to construct the parity check matrix. The lattice-cyclic property of these codes provides very efficient decoding of erasure bursts for these codes.      

Design and Factorization of Two-Channel Perfect Reconstruction Filter Banks with Causal-Stable IIR Filters

In this paper, new design and factorization methods of two-channel perfect reconstruction (PR) filter banks (FBs) with casual-stable IIR filters are introduced. The polyphase components of the analysis filters are assumed to have an identical denominator in order to simplify the PR condition. A modified model reduction is employed to derive a nearly PR causal-stable IIR FB as the initial guess to obtain a PR IIR FB from a PR FIR FB. To obtain high quality PR FIR FBs for carrying out model reduction, cosine-rolloff FIR filters are used as the initial guess to a nonlinear optimization software for solving to the PR solution. A factorization based on the lifting scheme is proposed to convert the IIR FB so obtained to a structurally PR system. The arithmetic complexity of this FB, after factorization, can be reduced asymptotically by a factor of two. Multiplier-less IIR FB can be obtained by replacing the lifting coefficients with the canonical signal digitals (CSD) or sum of powers of two (SOPOT) coefficients.     

过采样精确重构余弦调制滤波器组的设计

本文首先推导出过采样滤波器组精确重构的条件,由于此时所需的约束条件数比临界采样时少,因而可以设计出频域衰减特性更好的滤波器用,然后提出了精确重构约束条件下原型概通江波器的一种新的设计方法,采用矢的二次型约束优化算法,该算法优化方便,收剑速度快,与其它方法相比,滤波器的阻带衰减大。