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。     

任意阶正则线性相位小波滤波器的特征滤波器设计方法

小波滤波器的设计是小波分析的关键，本文给出了任意阶正则线性相位近正交小波滤波器的特征滤波器设计方法。     

B样条小波基在信号去噪中应用与性能分析

针对实际应用要求正交小波基具有一定的光滑性和正则性，利用B样条正交小波基构造滤波器，理论上通过对total variation这一正则性度量的计算，得出B样条小波的正则性优于Haar、shanonon小波，并且提出应用互相关算法来解决原信号和重构信号的延迟问题，实验分析表明：由其构造的滤波器应用在非突变信号下比Haar、shanonon小波基构造的滤波器的信噪比得到了显著性的提高。     

最小延迟M带余弦调制小波滤波器组设计

本文推导了最小延迟任意长度M带余弦调制小波滤波器组的完全重构条件。选择低通原型滤波器最大阻带衰减为优化的目标函数,通常的优化目标函数选用最小平方逼近的方法,本文提出了使用最佳一致逼近的方法。最后用黄金分割和牛顿迭代方法解决非线性约束优化极值问题,得到满足几乎完全重构和小波正则性条件的低通原型滤波器。     

任意阶正则线性相位小滤波器的特征滤波器设计方法

小波滤波器的设计是小波分析的关键。本文给出了任意２阶正则线性相位近正交小波滤波器的特征滤波器设计方法。     

两通道正则正交的主分量滤波器组设计

本文研究了两通道正则正交的主分量滤波器组设计.给出了正则乘积滤波器的参数表示,设计转化成标准的LSIP问题并且提出了一种适合于单参数和双参数可行解迭代算法.     

一类易于VLSI实现的对称双正交小波设计方法研究

该文提出了一类对称双正交小波的设计方法。该类双正交小波的小波滤波器组具有格形结构,实现该小波变换的分析滤波器组和综合滤波器组满足双正交条件和正则性条件,且设计的各滤波器均为实数二进制系数,因而该小波变换易于高速VLSI实现。文中的理论推导和设计实例,均验证了该设计方法的有效性。     

T—级联结构无源数字滤波器的实现

本文提出数字滤波器的结构无源T-级联实现的统一方法,使反对称和非对称滤波器的实数正则实现问题得以解决,并使波数字环形滤波器和波数字格形滤波器可在Z-域统一实现,已有的各种T-级联结构无源数字滤波器均可由本文方法得到。     

高正则二维小波的构造及在遥感图像编码中的应用

首先根据对称正交二维小波滤波器组的阶因式分解表示,结合正则性条件,建立一组以滤波器组参数为未知数的高阶多元多项式非线性方程组,并将这一组方程分解为两个子方程组,应用计算代数中的Groebner基算法分别求出解其Groebner基后获得二维小波滤波器组的全部参数,从而构造出一种集正交性、对称性和高正则性于一体的完美的"真"二维小波;其次从二维正交多分辨分析出发,推导出二维小波变换的分解和重构快速算法;最后将构造得到的3正则阶二维小波和SPIHT编码算法相结合对某地的遥感图像进行压缩编码.实验结果显示该方法具有较好的编码性能.     

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。      

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

$M$th-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat$R$-regular finite impulse response (FIR)$M$th-band filters with a specified integer group delay at$ omega =0 $is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat$R$-regular FIR$M$th-band filters via the blockwise waveform moments. Differing from the conventional FIR$M$th-band filters with exactly linear phase responses, the generalized FIR$M$th-band filters proposed in this paper have an arbitrarily specified integer group delay at$ omega =0 $. Moreover, a new efficient implementation of the generalized maxflat$R$-regular FIR$M$th-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR$M$th-band filters.     

Wavelet filter evaluation for image compression

Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2(L),2(L)). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design.     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

A novel approach to the design of the class of triplet halfband filterbanks

A new approach is presented for designing the recently introduced class of triplet halfband filterbank which are defined by three kernels. The Parametric Bernstein Polynomial is used to construct the kernels. The filterbanks have the advantage of structural perfect reconstruction and structural regularity. The design of the free parameters of the Bernstein Polynomial is achieved through a least squares method. A novel iterative procedure is employed to optimize the objective function which is a multiquadratic function of the free parameters. The design technique is flexible in that it allows filters with different characteristics to be designed with ease. Filter regularity can be traded for increased sharpness in the frequency response and regular scaling function and wavelets can be readily obtained.     

一类最佳数据压缩FIR滤波器与Daubechies 小波

提出了一种设计数据压缩FIR滤波器的新方法．该方法在不引入信息失真的前提下以最有效分解原信号为目的设计滤波器．由此设计的滤波器可以实现数据基于压缩目的的最优分解,能够最大可能地提取信号中的有用信息同时去除冗余信息．该分解过程与具有一定正则性的Daubechies小波的离散小波变换十分相似,该滤波器也和Daubechies小波分解滤波器完全相同,其原因是Daubechies在构造小波时引入的余项应为零．     

Design of efficient M-band coders with linear-phase andperfect-reconstruction properties

This paper presents a new design technique for obtaining M-band orthogonal coders where M=2ⁱ. The structures obtained using the proposed technique have the perfect reconstruction property. Furthermore, all filters that constitute the subband coder are linear-phase FIR-type filters. In contrast with conventional design techniques that attempt to find a unitary alias-component matrix in the frequency domain, we carry out the design in the time domain, based on time-domain orthonormality constraints that the filters must satisfy. The M-band design problem is reduced to the problem of finding a suitable lowpass filter h₀(n). Once a suitable lowpass filter is found, the remaining (M-1) filters of the coder are obtained through the use of shuffling operators on the lowpass filter. This approach leads to a set of filters that use the same numerical coefficient values in different shift positions, allowing very efficient numerical implementation of the subband coder. In addition, by imposing further constraints on the lowpass branch impulse response h₀(n), we are able to construct continuous bases of M-channel wavelets with good regularity properties. Design examples are presented for four-, eight-, and 16-band coders, along with examples of continuous wavelet bases that they generate     

New filter banks and more regular wavelets

One of the most interesting features of a wavelet is its Sobolev regularity. In this paper, we construct new wavelets that are more regular than the Daubechies wavelets for a given support width. We tabulate the coefficients of the new filters to make them easily accessible. We show that these filters outperform the Daubechies filters in the L² approximation of the ideal filter. An application for speech analysis, synthesis, and compression is provided     

具有紧支撑对偶的双正交插值子波系统正则度的优化设计

本文研究了对称内插尺度函数及其对偶的参数化表示。在此基础上,提出了一般插值子波系统的正则度优化设计方法和相应的Minimax优化算法。优化结果表明:内插尺度函数正则度的优化设计明显提高了系统的逼近能力;而对偶正则度的优化设计增加了对偶的光滑性,并且分析滤波器的通带,阻带特性也得到了显著的改善。     

A Globally Optimal Bilinear Programming Approach to the Design of Approximate Hilbert Pairs of Orthonormal Wavelet Bases

It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the lp (p=1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters. The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem. Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover, the designed orthogonal wavelet bases show that minimizing the l ₁ norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.