Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming

In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches.     

Design of High-Order Extrapolated Impulse Response FIR Filters with Signed Powers-of-Two Coefficients

Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied in the last three decades. However, most approaches for the design of FIR filters with SPT coefficients focus on filters with length less than 100. These approaches are not suitable for the design of high-order filters because they require excessive computation time. In this paper, an approach for the design of high-order filters with SPT coefficients is proposed. It is a two-step approach. Firstly, the design of an extrapolated impulse response (EIR) filter is formulated as a standard second-order cone programming (SOCP) problem with an additional coefficient sensitivity constraint for optimizing its finite word-length effect. Secondly, the obtained continuous coefficients are quantized into SPT coefficients by recasting the filter-design problem into a weighted least squares (WLS) sequential quadratic programming relaxation (SQPR) problem. To further reduce implementation complexity, a graph-based common subexpression elimination (CSE) algorithm is utilized to extract common subexpressions between SPT coefficients. Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients. Experiment results indicate that 0.81N∼0.29N adders are required for 18-bit N-order FIR filters (N=335∼3261) to meet the given magnitude response specifications.     

A Design of 2 L-Channel FIR Paraunitary Filter Banks with Complex Coefficients

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基于神经网络的4型FIR滤波器的优化设计

详细讨论了4型线性相位滤波器的幅频特性与正弦基函数神经网络算法的关系,分析了神经网络系统的稳定条件,给出了FIR滤波器优化设计实例。根据4型FIR滤波器的幅频响应特性,构造出一个相应的神经网络模型,并建立了FIR线性相位数字滤波器的神经网络算法。该算法通过训练神经网络权值,使设计的数字滤波器与希望得到的FIR线性相位滤波器的幅频响应之间的误差平方和最小化,从而获得FIR线性相位数字滤波器的脉冲响应。计算机仿真表明了该算法的有效性和优异性能。     

可变带宽FIR低通滤波器设计和RAG算法系数综合

提出使用简化加法器图算法综合可变带宽FIR数字滤波器。首先使用谱参数的方法建立可变带宽、线性相位的FIR低通数字滤波器的系统函数,通过使用加权最小均方的方法,得到了滤波器系数的最优表达式。然后基于可变滤波器结构为定系数FIR子滤波器线性组合的特点,提出使用筒化加法器图算法综合其硬件结构。该算法生成一种能最大程度地利用系数之间共享特性的加法器流图,使用较少的加法器个数和加法次数实现系数相乘。最后设计实例证明了可变带宽的有效性和该算法的高效性。     

1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Christoffel–Darboux formula for Chebyshev continual orthogonal polynomials of the first kind is proposed to find a mathematical solution of approximation problem of a one-dimensional (1D) filter function in the z domain. Such an approach allows for the generation of a linear phase selective 1D low-pass digital finite impulse response (FIR) filter function in compact explicit form by using an analytical method. A new difference equation and structure of corresponding linear phase 1D low-pass digital FIR filter are given here. As an example, one extremely economic 1D FIR filter (with four adders and without multipliers) is designed by the proposed technique and its characteristics are presented. Global Christoffel–Darboux formula for orthonormal Chebyshev polynomials of the first kind and for two independent variables for generating linear phase symmetric two-dimensional (2D) FIR digital filter functions in a compact explicit representative form, by using an analytical method, is proposed in this paper. The formula can be most directly applied for mathematically solving the approximation problem of a filter function of even and odd order. Examples of a new class of extremely economic linear phase symmetric selective 2D FIR digital filters obtained by the proposed approximation technique are presented.     

Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and Group delay constraints

In this paper, we formulate a general design of transversal filter structures with maximum relative passband-to-stopband energy ratio subject to complex frequency response constraints in the passband and the stopband as well as additional constraints such as constraints. These constraints are important for applications where the suppression of noise at certain frequencies are important. Additional constraints are introduced allowing approximately linear phase and constant group delay in the passband. For a given set of basis functions, the design problem can be formulated as a semi-infinite quadratic optimization problem in the filter coefficients, which are the decision variables to be optimized. In this paper, we focus on the design of digital Laguerre filter and digital finite impulse response (FIR) filter structures. A modified bridging algorithm is developed for searching for the optimum pole of the Laguerre filters. Design examples are given to demonstrate the effectiveness of the proposed algorithm.     

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.     

可编程FIR滤波器的FPGA实现

介绍了FIR滤波器的基本的线性相位结构及FIR滤波器的抽头系数SD算法编码。给定滤波器的数字指标,用MATLB设计抽头系数,最后用Verilog HDL语言实现了一个16阶的FIR低通滤波器并在QuartusⅡ上仿真,并对仿真结果与理论值进行比较,波形仿真结果和理论值相吻和,最后将编程数据文件下载到FPGA芯片上。对于不同性能的FIR滤波器,抽头系数是变化的,因此只要对本设计的抽头系数重新在线配置,就可以实现不同的FIR滤波器。     

基于SystemView数字滤波器设计的仿真与分析

SystemView是一个动态系统分析设计软件,具有强大的数字信号处理功能,文中介绍了基于SystemView数字滤波器的设计,它集IIR和FIR滤波器于一身,且IIR滤波器的模拟滤波器原型、FIR滤波器的窗函数及相关参数很容易通过设计界面进行设置。仿真结果表明,所设计出的滤波器符合设计要求和指标。     

A fast perturbation method for the design of linear phase fir digital filters of finite wordlength using single-frequency filters

In this paper a fast perturbation algorithm for the design of linear phase FIR digital filters of finite wordlength is presented. The original set of filter coefficients are obtained using the Parks-McClellan algorithm, then a small perturbation is given to these sets of coefficients. The peak deviations corresponding to the rounded set of coefficients obtained from the original and the perturbed sets are compared and the set of coefficients with the lower value of peak deviation is stored as the best set of coefficients. A further perturbation is given to the infinite precision coefficents and these are rounded to the required wordlength. Comparison is made between these rounded sets and the present best set with respect to peak deviation and the better set is stored as the best set of coefficients. This process is repeated for a finite number of times or until the peak deviation is sufficiently low. To obtain the compensating filter coefficients single-frequency filters are used. Mathematical justification for the single-frequency design is given. Important results for a large number of design examples are presented to illustrate the speed and effectiveness of the algorithm.     

一种低复杂度的稀疏FIR陷波滤波器的设计方法

FIR陷波滤波器具有线性相位、精度高、稳定性好等诸多优势,然而当陷波性能要求较高时,通常需要较高的阶数,导致FIR陷波滤波器硬件实现复杂度大大提高。该文基于稀疏FIR滤波器设计算法和共同子式消除的思想,提出一种低复杂度的FIR陷波滤波器设计方法。该方法首先采用稀疏滤波器设计算法得到满足频域性能设计要求的FIR陷波原始滤波器系数,然后对其进行CSD编码,并分析CSD编码量化系数集中所有的2项子式和孤子的灵敏度,最后根据灵敏度的大小依次选择合理的2项子式或孤子直接合成滤波器系数集。仿真结果表明,新算法设计实现的FIR陷波滤波器比已有的低复杂度设计方法最多可减少51%的加法器,有效地降低了硬件实现复杂度,大大节省了硬件资源。

     

基于MATLAB与CCS的FIR滤波器的C语言实现

为保证所设计的FIR数字低通滤波器具有严格的线性相位,在对几种FIR基本结构的比较之后,采用了线性相位FIR滤波器的直接型结构。使用Matlab内置函数计算出滤波器的系数和检验滤波器的频率响应特性。采用C语言实现数字滤波器的设计,并在集成开发环境代码调式器(Code Composer Studio,CCS)上进行仿真,仿真结果表明,所设计的数字低通滤波器能够满足系统实时性和不失真要求。     

Novel design strategy of multiplier-less low-pass finite impulse response filter using self-organizing random immigrants genetic algorithm

Intelligent optimization techniques are playing a very vital role in solving a wide variety of problems of engineering and technology of late. In order to meet the challenges from various perspectives, researchers are always in favor of applying those approaches to get rid of numerous practical difficulties of concern. Digital signal processing, more specifically the design of digital filters in particular, has been immensely motivated and beneficiated by means of this amalgamation. In this communication, we have incorporated a recently proposed genetic optimization method, named as self-organizing random immigrants genetic algorithm, in multiplier-free finite impulse response filter (FIR) design algorithm. Our study has focused on the selection of optimum settlement of filter coefficients through the utilization of this population-based technique which results in power of two distribution of impulse response over a binary search space. The performance of our designed filter has been thoroughly analyzed by a number of design parameters of interest and compared with other state-of-the-art multiplier-less FIR models. It has been observed that the proposed approach outperforms the other designs by a considerably large margin in those areas of signal processing where the reduction in hardware cost is the biggest challenge.     

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.     

基于Hanning Window设计FIR数字高通滤波器

基于实序列的傅里叶变换具有的特征,提出了一种研究线性相位FIR数字滤波器幅度函数的简洁方法。首先揭示了偶对称和奇对称的线性相位FIR数字滤波器幅度函数的特点;然后研究了矩形窗函数对线性相位理想数字低通滤波器幅频特性的影响,即时域加矩形窗,频域形成过渡带;最后介绍了利用窗函数法设计FIR数字滤波器时,对窗函数的要求,选择窗函数的依据及利用窗函数法设计FIR数字滤波器的步骤,并给出了基于Hanning Window来设计FIR数字高通滤波器的实例。     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

基于MATLAB和DSP的数字滤波器设计

介绍了有限冲激响应（FIR,Finite Impulse Response）数字滤波器的原理以及如何根据给定的技术指标设计所需的FIR数字滤波器。运用MATLAB软件提供的滤波器设计工具FDATool得到滤波器的系数,在CCS集成开发环境下,完成了线性移位缓冲区法的FIR滤波器的软件仿真。仿真结果表明：滤波器达到了给定...     

An unbiased p-step predictive FIR filter for a class of noise-free discrete-time models with independently observed states

The paper addresses a new unbiased p-step toward predictive finite impulse response (FIR) filter for a class of discrete-time deterministic state space models, which states are represented on a horizon of N past points with degree polynomials and observed independently. It is implied that measurements are not available at a current time point n. The problem arises in synchronization and tracking when a signal is lost. Generic coefficients are derived via the Bernoulli polynomials for a two-parameter family of the polynomial filter gains. A generalization is provided for the linear (ramp) and quadratic filter gains. We show that the solution proposed is efficient in applications to predictive filtering of the states of local clocks of digital communication network nodes when a synchronizing signal is temporarily not available.