一种二阶锥规划通带线性相位FIR滤波器的设计

在有限冲激响应（Finite Impulse Response,FIR）滤波器设计中,如果系统只要求通带或某个频域区间具有线性相位而其他频域区间相位非线性,则系数对称的FIR滤波器设计方法不再适用。为此,提出了一种基于二阶锥规划（Second-Order Cone Programming,SOCP）的通带线性相位FIR滤波器设计方法。该方法使用二阶锥规划实现滤波器设计,其中优化目标为通带最小群延迟,约束条件为全频域振幅误差。实验结果显示,所提方法设计的FIR滤波器有着很好的幅频特性和通带线性相位,通带群延迟误差很小。该方法实现简单,计算复杂度低,可以广泛应用于数字信号处理领域。     

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.     

低复杂度FIR数字滤波器设计方法

FIR滤波器具有绝对稳定性和线性相位的优势,然而当对滤波器的频域性能要求较高时,FIR滤波器通常需要很高的阶数,这使得FIR滤波器硬件执行的复杂度很高。为降低FIR滤波器的硬件执行复杂度,诸多研究者进行了探索。文章对低复杂度FIR滤波器设计方法进行研究,着重介绍比较典型的频率响应罩设计方法、外插脉冲响应设计方法和基于压缩感知的设计方法。     

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.     

数字FIR滤波器的设计与实现

数字滤波器是一种用来过滤时间离散信号的数字系统，通过对抽样数据进行数学处理来达到频域滤波的目的。根据其单位冲激响应函数的时域特性可分为两类：无限冲激响应（IIR）滤波器和有限冲激响应（FIR）滤波器。与IIR滤波器相比，FIR的实现是非递归的，它总是稳定的，更重要的是，FIR滤波器在满足幅频响应要求的同时，可以获得严格的线性相位特性。因此，它在高保真的信号处理，[第一段]     

3型FIR高阶多通带滤波器的自适应优化设计研究

本文详细讨论了3型线性相位滤波器幅频特性与正弦基神经网络算法间的关系，提出了该算法的收敛定理，给山了有限脉冲响应（FIR）高阶多通带滤波器自适应优化设计算法及实例。计算机仿真结果表明了该算法在FIR高阶多通带滤波器的有效性和优异性能。     

一维线性相位FIR数字滤波器的领域最小平方误差设计方法

本文提出了一种设计一维线性相位ＦＩＲ数字滤波器的新方法。该方法采用的频域的最小平方误差函数使所求的增益特性逼近所希望的增益特性，其计算公式非常简单，并可设计任意形状增益特性的ＦＩＲ数字滤波器。设计产例表明提出的方法非常有效。     

具有任意频响的二维FIR数字滤波器设计的闭式最小二乘解

本文研究具有任意频响特性的二维ＦＩＲ数字滤波器的最小二乘设计问题。     

二阶锥规划方法对于低群延时复系数有限冲激响应数字滤波器优化设计

针对低群延时复系数有限冲激响应数字滤波器优化设计问题,提出了一种幅度和相位独立约束的等纹波设计新方法.该方法在相位误差一定的条件下对幅度的上界和下界分别采取复数圆约束和线性不等式约束,不仅提高了幅度约束的精度,而且将非凸的滤波器设计问题转化为二阶锥规划问题;同时,为抑制通带边缘附近较大的群延时震荡效应,引入了相位误差一...     

基于FIR与相位补偿IIR滤波器的雷达回波信号处理

FIR与IIR频率选择滤波器的设计,被广泛应用于数字信号处理领域之中。文章以雷达回波信号的数字处理为例,首先分别设计FIR,IIR滤波器完成了对信号特定频率分量的滤除。进而,针对IIR滤波器的非线性相位,基于最优化设计全通系统实现了相位补偿,并对FIR,IIR滤波器进行了综合比较。     

Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay

An efficient coefficient quantization scheme is described for minimizing the cost of implementing fixed parallel linear-phase finite impulse response (FIR) filters in the modified Farrow structure introduced by Vesma and Saramaki for generating FIR filters with an adjustable fractional delay. The implementation costs under consideration are the minimum number of adders and subtracters when implementing these parallel subfilters as a very large-scale integration (VLSI) circuit. Two implementation costs are under consideration to meet the given criteria. In the first case, all the coefficient values are implemented independently of each other as a few signed-powers-of-two terms, whereas in the second case, the common subexpressions within all the coefficient values included in the overall implementation are properly shared in order to reduce the overall implementation cost even further. The optimum finite-precision solution is found in four steps. First, the number of filters and their (common odd) order are determined such that the given criteria are sufficiently exceeded in order to allow some coefficient quantization errors. Second, those coefficient values of the subfilters having a negligible effect on the overall system performance are fixed to be zero valued. In addition, the experimentally observed attractive connections between the coefficient values of the subfilters, after setting some coefficient values equal to zero, are utilized to reduce both the implementation cost and the parameters to be optimized even more. Third, constrained nonlinear optimization is applied to determine for the remaining infinite-precision coefficients a parameter space that includes the feasible space where the given criteria are met. The fourth step involves finding in this space the desired finite-precision coefficient values for minimizing the given implementation costs to meet the stated overall criteria. Several examples are included illustrating the efficiency of the proposed synthesis scheme.     

基于神经网络方法的可变分数延迟FIR滤波器设计

本文提出了设计可变分数延迟FIR滤波器的一种神经网络优化方法。首先建立一个连续Hopfield神经网络模型,通过选择网络的Lyapunov能量函数与优化目标问题的最小均方误差函数相一致的关系得到系统的最优解。仿真结果表明,在计算代价略有增加的情况下,其性能优于加权最小二乘方法。     

最小平方误差受限的FIR滤波器设计

在设计FIR滤波器时,往往会指定过渡带大小,但过渡带的引入只是为了便于滤波器的设计,而并不是物理上的需要,所以在设计中仅需指定截至频率。这是第一个设计理念。此外,在FIR滤波器的设计中存在两种准则:一是等波纹设计准则 (即最大误差最小化或者Chebyshev准则 ),另一种是平方误差最小准则。但在现实中两种准则往往要同时兼顾,所以仅基于其中一种准则来设计不能得到最佳结果。这是第二个设计理念。基于上述两种设计理念,提出了一种新的FIR滤波器设计算法。该算法采用最陡梯度下降法来对平方误差最小化下的最佳滤波器系数进行迭代修正,得到最佳结果。     

Optimal Design of Nonlinear-Phase FIR Filters With Prescribed Phase Error

Constrained least-squares design and constrained Chebyshev design of one- and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-definite quadratic programming approach. In order to obtain unique optimal solutions, we propose to impose constraints on the complex approximation error and the phase error. By introducing a sigmoid phase-error constraint bound function, the group-delay error can be greatly reduced. A Goldfarb–Idnani based algorithm is presented to solve the semi-infinite positive-definite quadratic program resulting from the constrained least-squares design problem, and then applied after some modifications to the constrained Chebyshev design problem, which is proved in this paper to be equivalent also to a semi-infinite positive-definite quadratic program. Through design examples, the proposed method is compared with several existing methods. Simulation results demonstrate the effectiveness and efficiency of the proposed method.      

基于信号空间的最佳FIR分数延迟滤波器的设计方法

分数延迟滤波器广泛用于通信,语音处理,回声消除等。该文基于信号的多分辨空间一般模型,由尺度函数给出最优FIR分数延迟滤波器的设计方法,并进行数值试验证实其有效性。     

Optimal Design of Frequency-Response Masking Filters With Reduced Group Delays

In this paper, a new method for the design of optimal finite-impulse response frequency-response masking (FRM) filters with reduced passband group delays is proposed. To meet the prescribed magnitude response and group delay, the proposed design method takes into account both the magnitude error and the group delay error. The key step is the derivation of the group delay and its gradient with respect to the filter coefficients, based on which an explicit group delay constraint is formulated. By incorporating the group delay constraint into the overall optimization, FRM filters with better approximation to the prescribed reduced group delay can be obtained in comparison with a recent method by Lu and Hinamoto in 2003, as illustrated by two design examples.      

带约束的复FIR数字滤波器Chebyshev设计算法

本文主要讨论了复FIR数字滤波器的频域不等式约束Chebyshev设计问题.作者首先把文献[1]中的复交错点组定理扩展到有不等式约束的情况,之后根据扩展定理中对最优解特性的描述,并结合复Remez算法[1]及赖晓平的迭代Remez算法[2][3],提出了一种有效的算法来解决频域带不等式约束的复FIR数字滤波器的Chebyshev设计问题.如果问题的解存在,则算法能保证收敛到最优解.作者用MATLAB语言对上述算法进行了实现并做了仿真分析.     

On the Design of FIR Filters with Powers-of-Two Coefficients

FIR filters with powers-of-two coefficients are attractive for cost-effective implementations. The performance of one such structure, the difference routing digital filter [8], is discussed. Using an SNR criterion, an optimal algorithm to select the value of the filter coefficients is presented. Results indicate that a 2-3 dB improvement in the SNR can be obtained with this new approach. In addition, the study gives some insight into the relationship between the filter sampling rate, the number of coefficients, and the size of the coefficient alphabet. In particular, it is seen that a tradeoff between the filter sampling rate and the size of the coefficient alphabet exists.     

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.