Design of Real FIR Filters With Arbitrary Magnitude and Phase Specifications Using a Neural-Based Approach

An efficient and yet simple neural-based approach is utilized to design real finite-impulse response filters with arbitrary complex frequency responses in the least-squares sense. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. To achieve good convergences for large filter lengths, a cooling process of simulated annealing is used for the neural activation function. Several examples and comparisons to the existing methods are presented to illustrate the effectiveness and flexibility of the neural-based method     

Cooperative Coevolutionary Genetic Algorithm for Digital IIR Filter Design

A novel algorithm for digital infinite-impulse response (IIR) filter design is proposed in this paper. The suggested algorithm is a kind of cooperative coevolutionary genetic algorithm. It considers the magnitude response and the phase response simultaneously and also tries to find the lowest filter order. The structure and the coefficients of the digital IIR filter are coded separately, and they evolve coordinately as two different species, i.e., the control species and the coefficient species. The nondominated sorting genetic algorithm-II is used for the control species to guide the algorithms toward three objectives simultaneously. The simulated annealing is used for the coefficient species to keep the diversity. These two strategies make the cooperative coevolutionary process work effectively. Comparisons with another genetic algorithm-based digital IIR filter design method by numerical experiments show that the suggested algorithm is effective and robust in digital IIR filter design     

用模拟退火法设计数字滤波器

研究了用模拟退火的优化算法来设计数字FIR滤波器,提出了一种针对FIR滤波器设计的优化改进方法,该方法提高了搜索全局最优的能力,并显著缩短了优化计算时间。     

FIR Photonic Microwave Filter Design Employing Simulated Annealing Algorithm

Photonic microwave filters are important parts of fiber‐optic microwave/millimeter wave processing systems. In this paper, the synthesis problem of fiber‐optic FIR microwave filters is addressed and a novel method for designing photonic microwave filter employing a simulated annealing (SA) algorithm is proposed. The design problem of photonic microwave filter can be reduced to be a multi‐variable function optimization problem, which can be solved by a simulated annealing‐based algorithm. As an illustration of the application of SA to photonic microwave filter design, the synthesis of an optimizedFBG‐based photonic microwave filter is discussed. Numerical results show that the global minimum finding capability of SA makes it be an efficient way to design the photonic microwave filter. Numerical results also demonstrate that the proposed method can be applied to design different filtering systems with different constraints.     

Applications of simulated annealing for the design of specialdigital filters

The authors describe the salient features of using a simulated annealing (SA) algorithm in the context of designing digital filters with coefficient values expressed as the sum of power of two. A procedure for linear phase digital filter design, using this algorithm, is presented and tested, yielding results as good as those for known optimal methods. The algorithm is then applied to the design of Nyquist filters, optimizing at the same time both frequency response and intersymbol interference, and to the design of cascade form finite-impulse-response (FIR) filters. The drawback of using SA is that the computation time is on the order of 1-2 h for each filter design, on the Sun 3/60. However, this was more than compensated by the versatility of the new algorithm, which can be used to design filters with multiple constraints     

Design of IIR eigenfilters in the frequency domain

The eigenfilter approach is an appealing way of designing digital filters, mainly because of the simplicity of its implementation. In this correspondence, a new method of applying the eigenfilter approach to the design of infinite impulse response (IIR) filters is described. The procedure works in the frequency domain and yields the coefficients of a causal rational transfer function having an arbitrary number of poles and zeros. Some examples of filter design are given to show the effectiveness of the method presented     

A fast algorithm for FIR digital filtering with a sum-of-triangles weighting function

A doubly recursive algorithm for time domain convolution with a piecewise linear weighting function is presented that combines the speed of a recursive (IIR) digital filter with the flexibility and ease of design of a nonrecursive (FIR) digital filter. The approach approximates the desired FIR weighting function by a sum-of-triangles weighting function. ForL triangles (or triangle pairs for a linear phase filter) the algorithm is of orderLN. The approximation improves with the number of triangles. A significant advantage of the algorithm compared to FFT filtering or direct convolution is that there is no necessity of a tradeoff between frequency response accuracy and computation time per output point as the data spacing decreases in the filtered signal. The computational complexity is dependent on the number of triangles chosen, not the width of the weighting function, so the algorithm is especially effective for filters with an inherently wide FIR weighting function.     

A WISE method for designing IIR filters

The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces the quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature     

基于遗传退火算法的MTI 滤波器设计方法

动目标显示(MTI)是雷达杂波抑制的重要技术之一,MTI 滤波器系数和脉冲参差比设计对MTI 的抗杂波性能至关重要。遗传退火算法将模拟退火算法过程溶入遗传算法,同时克服了遗传算法容易陷入局部最优和模拟退火算法收敛速度慢的缺点。文中介绍了一种将遗传退火算法应用于MTI 滤波器的设计方法,该方法可找到最优MTI 滤波器。实验结果表明,针对给定的MTI 滤波器设计要求,该方法能快速完成优化遍历,优化后滤波器性能提升明显。     

A Hybrid system for the reconstruction of a smooth function from its samples

The long-standing problem of reconstructing a function from its samples is considered again. Assuming a sequence of oversampled values, a set of appropriate idealized reconstruction filters can be defined, which do not suffer from instability or slow convergence. The realization — a cascade of a nonrecursive digital filter, D/A-converter, and a fixed/analog smoothing filter — demands the design of the digital filter for the increase of the sampling rate. The design of this nonrecursive filter is the purpose of this paper. Approximations in the frequency as well as in the time domain are presented.     

On the approximation of the magnitude response of two-dimensional IIR digital filters using linear programming

The design of two-dimensional IIR digital filters is approached using linear-programming techniques. The problem is formulated as an approximation problem and filter frequency response characteristics are represented via the square of the magnitude of the filter transfer function. An appropriate approximation error is minimized leading to a linear problem formulation. The latter problem does not require differential correction methods for its solution, thus resulting in a computationally efficient algorithm. Stability conditions and symmetry considerations are easily accounted for. The linear programming approach assures convergence of the solution to a global minimum, among other advantages over nonlinear methods. Several examples illustrate the strength and effectiveness of the methodology.     

一种高性能内插滤波器的设计

在全数字接收机系统中,随着高阶调制解调技术的应用,传统内插滤波器的性能已不能满足要求。为此,通过研究一种多项式函数的频率响应,提出了一种高性能内插滤波器的设计方法。该方法在频域逼近的基础上,以线性加权的最小均方误差（MMSE）为优化准则,利用Matlab系统函数进行线性约束条件下的最优化迭代,设计非常灵活。仿真结果表明,该方法设计的内插滤波器性能明显优于常用的内插滤波器,尤其适合于高阶正交幅度调制（QAM）信号。     

Optimal spectral windows for microwave diversity imaging

Tomographic microwave diversity imaging is analyzed using linear system theory concepts, and optimal spectral windows for data acquisition are obtained either by considering window position in the spectral domain or by using simulated annealing to find an optimal phase weighting of the object frequency response samples collected over the specified spectral window. This study provides a means of microwave image formation that is applicable under general assumptions. Results of numerical simulations and representative images reconstructed from realistic experimental microwave scattering data are given, demonstrating that the proposed approach is superior to previous image reconstruction methods     

二相编码信号旁瓣抑制的频域处理方法

本文研究了雷达脉冲压缩信号中二相编码的距离旁瓣抑制问题，分析了二相码的频谱结构，采用频域数字处理技术，提出了一种基于网络综合的旁瓣抑制滤波器（SSF）的频域设计方法。并以15位M编码为例，对SSF的处理性能进行仿真分析。通过仿真实验表明，使用这种方法，能够达到非常理想的副瓣指标。     

An iterative algorithm for optimal design of non-frequency-selective FIR digital filters

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response （FIR） digital filters based on the windowing method. Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter, the key idea of the algorithm is minimizing the approximation error by successively modifying the design result through an iterative procedure under the condition of a fixed window length. In the iterative procedure, the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration. Because the approximation error can be specified variably, the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain. A design example is employed to illustrate the efficiency of the algorithm.     

快速傅立叶变换辅助设计数字低通滤波器

详尽讨论了快速傅立叶变换(FFT)应用于有限冲击响应(FIR)数字低通滤波器(DLPF)的设计和分析方法.应用FFT算法,将理想DLPF幅频特性转换到变换域,获得其变换域序列;设计窗函数对该序列开窗,获得FIR有限序列;应用快速傅立叶逆变换(IFFT)对其进行变换,获得相应窗函数可实现DLPF幅频特性.结果发现,FFT算法可获得与传统卷积算法相同的结果;不需要推算窗函数的频谱解析表达式;可以处理Kaiser窗等变换域解析式复杂、频域解析式难以精确求解的窗函数设计与分析.与传统的卷积分析法相比,FFT不仅算法简单、灵活,而且处理能力强,是分析FIR DLPF设计的有力工具.     

全相位DFT数字滤波器的设计与实现

本文提出了全相位数据空间的概念,并基于DFT/IDFT滤波导出了一种新型的零相位滤波器——全相位DFT(APDFT)数字滤波器.本文给出了它的脉冲响应与相应的DFT滤波响应向量之间的正、反变换公式,证明了这种滤波器的一些重要性质.APDFT方法兼有窗函数法和频率采样法的优点,是一种设计FIR滤波器的新方法.理论分析和模拟实验证实,其总体性能优于传统方法.APDFT数字滤波器除可用通常的卷积结构实现外,也可用一种直接频域网络实现.本文给出了这种网络结构及其简化算法.这种网络具有实时自设计功能.它可以构成时变系统用于滤波器传递函数实时可变的场合,可以方便地集成为一个长度和频响均可编程的通用零相位数字滤波器,而且还可用于实现严格互补子带滤波.     

A direct approach to the design of QMF banks via frequency domainoptimization

This paper studies the design of quadrature mirror filter (QMF) banks via frequency domain optimization. A direct approach is adopted that gives the necessary and sufficient condition for perfect reconstruction (PR). While analysis filter banks are designed to achieve frequency domain specifications required for subband coding, synthesis filter banks are designed to minimize the reconstruction error in frequency domain. The criterion used to measure the reconstruction error is H_∞ or Chebyshev norm (sup-norm). State-space solutions are derived for the H_∞ optimization, and numerical algorithms are developed to obtain the optimal synthesis filter bank. Moreover, the asymptotic PR property is established for optimal H_∞ solution of the synthesis filter bank     

Design of minimum-phase digital filters as the sum of two allpass functions using the cepstrum technique

A new and practical approach using the cepstrum technique is proposed in the design of minimum-phase digital filters as the sum of two allpass functions. The desired magnitude response is specified in the frequency domain. Its corresponding minimum-phase response is then obtained from the desired magnitude response. The desired phases for the two allpass filters are obtained from the magnitude and phase responses. For both filters to be stable, the corresponding denominator polynomials are minimum phase. The filter coefficients are obtained from the desired phases using the cepstrum technique. Design examples show that the method works well for both classical filter specification and general magnitude specification in the frequency domain.     

基于模拟退火遗传算法的微波光子滤波器特性研究

采用模拟退火遗传算法,分析了非等间距低通滤波器不同抽头下全正对称系数及含负系数的微波光子滤波器的频率响应特性,并与窗函数法进行了对比分析。仿真结果表明:全正对称系数条件下,带抽头数量越大,滤波器的优化性能越好。正负系数滤波器的对比表明,含负系数的滤波器优化性能明显改善,特别是对低通滤波器而言,系数的全正性极大地限制了光学传递函数的取值范围,影响了滤波器的性能。在同一截止频率下,模拟退火遗传算法优化性能指标略好于窗函数法。如果限制通带和阻带的截止频率,即放宽对过渡带的要求,模拟退火遗传算法性能优势更加明显。