二维线性相位FIR滤波器设计的投影最小二乘算法

考虑二维线性相位矩形对称FIR滤波器的约束最小二乘设计问题,即在通带和阻带逼近误差不超过给定值的约束下使逼近误差平方和最小.提出一个投影最小二乘算法,它是一个交替地更新有效约束集及将二次误差无约束极小点(最小二乘解)逐次投影到有效约束边界的迭代过程.通过二维FIR低通圆形滤波器和方形滤波器的设计例子,对算法的性能进行了仿真,并与基于内点算法和有效集方法的设计程序进行了比较,结果表明本文算法具有很高的效率.     

基于遗传算法的FIR滤波器设计

提出一种FIR数字滤波器的优化设计方法,即将遗传算法应用于频率采样法的FIR数字滤波器设计中。结合给定的FIR数字带通滤波器的技术指标,用遗传算法得到频率采样法中过渡带的最佳采样值,并分别用遗传算法与查表法对过渡带中采样点的频率采样法进行仿真实现。实验结果表明,采用遗传算法设计FIR数字滤波器可获得最大的阻带最小衰减,从而解决了传统查表法不能保证最优的问题。     

二维半平面线性相位FIR数字滤波器的最小二乘设计方法

本文研究了二维线性相位实系数FIR数字滤波器的最小二乘设计问题，导出了滤波器系数的闭式解。运用给出的计算公式可方便地计算滤波器的系数，而不必对矩阵进行数值求逆运算也不需要复杂的优化过程．设计实例表明本文给出的方法程序简单、计算时间极短．     

二维线性相位FIR数字滤波器的优化设计

该文提出了一种用神经网络算法来设计二维线性相位数字滤波器的新方法。通过分析二维FIR线性相位滤波器的幅频响应特性,建立了神经网络算法。根据给定的幅频响应指标,按该算法可获得滤波器系数。为保证该算法的稳定性,提出并证明了该算法的收敛定理。文中给出了圆对称和矩形对称二维低通线性相位FIR数字滤波器优化设计实例。计算机仿真结果表明由该方法设计的二维数字滤波器,通带和阻带范围波动小,所需计算量非常少,稳定性强,因而是一种优异的设计方法。     

Algebraic Design of Some Equiripple Linear-Phase Half-Band FIR Filters

A closed form solution for the approximation of a linear-phase FIR (finite impulse response) filter with equiripple magnitude responsein the passband and stopband was not known. In this letter we present a closed form solution of some equiripple linear-phase half-band FIR filter approximation.     

Potential of Particle Swarm Optimization and Genetic Algorithms for FIR Filter Design

This article studies the performance of two metaheuristics, particle swarm optimization (PSO) and genetic algorithms (GA), for FIR filter design. The two approaches aim to find a solution to a given objective function but employ different strategies and computational effort to do so. PSO is a more recent heuristic search method than GA; its dynamics exploit the collaborative behavior of biological populations. Some researchers advocate the superiority of PSO over GA and highlight its capacity to solve complex problems thanks to its ease of implementation. In this paper, different versions of PSOs and GAs including our specific GA scheme are compared for FIR filter design. PSO generally outperforms standard GAs in some performance criteria, but our adaptive genetic algorithm is shown to be better on all criteria except CPU runtime. The study also underlines the importance of introducing intelligence in metaheuristics to make them more efficient by embedding self-tuning strategies. Furthermore, it establishes the potential complementarity of the approaches when solving this optimization problem.     

等式约束FIR滤波器设计的投影最小二乘算法

本文考虑具有频域和时域等式约束的FIR滤波器设计问题,提出一个非常有效的新算法——投影最小二乘算法.该算法由两部分组成,前一部分产生一个解析的最小二乘解,后一部分将此解逐次投影到每个等式约束上.该算法有两个显著特点:一是目标函数的Hessian矩阵不要求正定;二是由于采用平方根因子分解来计算增广Hessian矩阵及投影算子矩阵,算法具有很好的数字稳定性.以此算法为核心构成了一个迭代算法,用于实现FIR Nyquist滤波器的minimax设计.设计例子表明了所提算法的有效性和数字稳定性.     

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.      

Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

In this work, a greedy algorithm for the design of sparse linear-phase finite impulse response filters wherein the coefficients are successively fixed to zero individually is proposed. To meet the filter specifications, the coefficient for which the middle value of its feasible range is closest to zero is selected to be set to zero, whereas all the other unfixed coefficients are free to change. Design examples show that the proposed technique can design FIR filters with higher sparsity than that obtained by existing nonexhaustive algorithms for given specifications. To show the optimality of the algorithm, we design 100 filters, with results showing that the global optimal solution, i.e., the sparsest solution found by exhaustive search, can be achieved in most cases, but with much less computation time.     

Chebyshev Design of Linear-Phase FIR Filters With Linear Equality Constraints

By using basis transformation, the Chebyshev approximation of linear-phase finite-impulse response (FIR) filters with linear equality constraints can be converted into an unconstrained one defined on a new function space. However, since the Haar condition is not necessarily satisfied in the new function space, the alternating property does not hold for the solution to the resulted unconstrained Chebyshev approximation problem. A sufficient condition for the best approximation is obtained in this brief, and based on this condition, an efficient single exchange algorithm is derived for the Chebyshev design of linear-phase FIR filters with linear equality constraints. Simulations show that the proposed algorithm can converge to the optimal solution in most cases and to a near-optimal solution otherwise. Design examples are presented to illustrate the performance of the proposed algorithm.     

The Design of Linear-Phase FIR Multiple-Notch Filters with Variable Notch Frequencies

In this paper, a paradigm is developed to design the linear-phase FIR multiple-notch filters with variable notch frequencies. The design procedure can be proceeded through two steps: First, a linear-phase narrow-band low-pass filter met the given bandwidth and stopband ripple specifications is designed. Second, a tuning procedure is applied to the computed low-pass filter to yield the desired multiple-notch filter. When the notch frequencies are varied, the same tuning procedure can be employed to render the multiple-notch filter with the new set of the notch frequencies. The tuning procedure employed reduces the computational complexity of designing the multiple-notch filter with the new set of the notch frequencies. The simulation results demonstrate the effectiveness of our scheme.     

遗传算法在FIR滤波器设计——频率抽样法中的应用

本文介绍了遗传算法在FIR滤波器设计——频率抽样法中的应用.用遗传算法确定过渡带样本值,解决了传统方法(查表法)不能保证数据是最优的问题.本文还对标准遗传算法进行了适当的改进.给出了FIR数字低通、带通滤波器设计的两个例子.实验结果说明通过遗传算法设计的FIR滤波器性能较查表法得到了改善.     

An L1-Method for the Design of Linear-Phase FIR Digital Filters

This paper considers the design of linear-phase finite impulse response digital filters using an L₁ optimality criterion. The motivation for using such filters as well as a mathematical framework for their design is introduced. It is shown that L₁ filters possess flat passbands and stopbands while keeping the transition band comparable to that of least-squares filters. The uniqueness of L₁-based filters is explored, and an alternation type theorem for the optimal frequency response is derived. An efficient algorithm for calculating the optimal filter coefficients is proposed, which may be viewed as the analogue of the celebrated Remez exchange method. A comparison with other design techniques is made, demonstrating that the L₁ approach may be a good alternative in several applications.     

线性完全重构的二维滤波器组的Groebner基设计

为设计线性完全重构的二维滤波器组,引用了计算代数中的Groebner基方法,根据线性相位条件和完全重构条件,分别设计出二维滤波器组的分析滤波器和综合滤波器的多相元矩阵,给出其参数化形式。根据小波构造理论,利用所设计的分析滤波器组构造出一个对称的纯二维小波。设计结果显示了Groebner基方法的有效性,设计方法更为简单。     

基于模块局部可重构FIR滤波器设计

介绍了一种使用动态局部重构技术设计可重构FIR数字滤波器的方法,是一种注重面积效率高、灵活性强,允许动态插入或删除局部模块的方法,并在Xilinx Virtex-4 FPGA上实现.这种设计方法比传统的FIR滤波器的设计方法具有占用资源更少、重构时间更短、高速灵活性等优点.     

一种设计对数FIR数字滤波器的方法

本文提出了一种设计具有等波纹对数幅度响应的线性相位ＦＩＲ数字滤波器的方法,该设计方法以多次交换算法为基础。在给定通带与阻带误差比、通带误差和阻带误差三种情况下讨论该设计方法。介绍几个低通对数ＦＩＲ滤波器的设计例子,来说明该设计方法的效率。     

用频率采样法设计FIR滤波器

窗函数法和频率采样法是两种较为典型的FIR数字滤波器设计方法。目前,相关的《数字信号处理》教科书对窗函数法设计FIR滤波器进行了较为详细的论述,但对用频率采样法设计FIR滤波器这部分内容讲解得不够细致,让初学的学生感到难以理解。针对用频率采样法设计FIR滤波器的相关问题进行了较为深入的探讨,并结合实例借助Matlab软件进行了仿真和验证。仿真结果表明,选择合适的过渡采样点和滤波器长度,可以有效地控制阻带衰减、过渡带宽及计算复杂度。     

分布式算法在FIR数字滤波器实现中的应用

文章提出了一种利用FPGA实现FIR数字滤波器的设计方案,在设计过程中应用了分布式算法(DA).FPGA有着规整的内部逻辑阵列和丰富的连线资源,特别适合于数字信号处理任务.分布式算法(DA)是一项重要的FPGA技术,它使得在FPGA中实现FIR滤波器的关键运算--乘加运算,转化为了查找表,大大提高了FIR滤波器的速度.文中给出了VHDL语言编写的程序和仿真波形.     

一种改进型的FIR数字滤波器设计

探讨了FIR数字滤波器的传统设计方法,即先用Matlab进行方案设计和算法设计与验证,然后将此算法用DSP汇编语言实现,并在硬件DSP目标板上实现。分析了传统设计过程中的一些弊端,进而提出了一种改进型的FIR滤波器设计方法,即基于Matlab的DSP系统级设计方法。此方法将Matlab和TI CCS及目标DSP连接起来,使系统的设计过程得到了很大简化,方便了开发设计。