Digital IIR Integrator Design Using Richardson Extrapolation and Fractional Delay

In this paper, a new design of digital integrator is investigated. First, the trapezoidal integration rule and differential equation are applied to derive the transfer function of the digital integrator. The Richardson extrapolation is then used to generate high-accuracy results while using low-order formulas. Next, the conventional Lagrange finite-impulse response fractional delay filter is directly applied to implement the designed integrator. Two implementation structures are studied: direct substitution and polyphase decomposition. Finally, numerical comparisons with conventional digital integrators are made to demonstrate the effectiveness of this new design approach.      

Using New Hybrid Integrators to Design IIR Fractional-Order Integrators via Impulse Invariance Method

This paper presents a method for designing fullband and non-fullband IIR digital integrators with linear phase that has been used to approximate fractional-order integrators with IIR filters. Several numerical integration rules have been considered in this study, namely, Euler, Simpson, Schneider, bilinear, and F₀₁₂. The main idea in our design is based on interpolating the well-known integration rules (Euler, Bilinear and Simpson) proposed by Al-Alaoui combined with deterministic signal modeling techniques. Numerical examples are presented to illustrate the performance of the proposed integrators. It was found that the Euler–Simpson integrator gives better approximation accuracy than existing integrators.     

Closed-Form Design of Half-Sample Delay IIR Filter Using Continued Fraction Expansion

In this paper, the closed-form design of half-sample delay infinite-impulse response (IIR) filter is presented. First, the continued fraction expansion (CFE) and its recursive computation are reviewed briefly. Then, the CFE of square root function is applied to design half-sample delay IIR filters with various orders. The comparisons with conventional maximally flat half-sample delay all-pass and Lagrange filters are made and implementation issue is also addressed. Next, the designed half-sample delay filter is used to reduce the approximation error of the conventional IIR Simpson integrator, to design half-band and diamond shaped filters, and to magnify the digital image. Finally, several numerical examples are illustrated to demonstrate the effectiveness of the proposed design method     

基于MATLAB的IIR数字滤波器设计研究

IIR数字滤波器属于经典数字滤波器的一种，详细描述了利用功能强大的MATLAB编程语言设计IIR数字滤波器的方法和步骤。     

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.     

IIR数字粉红噪声滤波器的优化设计

提出了用遗传算法优化IIR数字滤波器的传递函数，使其幅频响应曲线的斜率逼近一3dB／oct。用优化得到的数字滤波器对白噪声序列滤波即可获得粉红噪声。试验结果表明，用遗传算法优化得到的IIR滤波器的频响与理想的-3dB/oct曲线吻合得很好。     

Minimax Design of IIR Digital Filters Using SDP Relaxation Technique

This paper presents a new algorithm using semidefinite programming (SDP) relaxation to design infinite impulse response digital filters in the minimax sense. Unlike traditional design algorithms that try to directly minimize the error limit, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit of the approximation error. Given a fixed error limit at each iteration, the SDP relaxation technique is adopted to formulate the design problem in a convex form. In practice, the true minimax design cannot be always obtained. Thus, a regularized feasibility problem is adopted in the bisection searching procedure. The stability of the designed filters can also be guaranteed by adjusting the regularization coefficient. Unlike other sequential design methods, the proposed algorithm tries to find a feasible solution at each iteration of the sequential design procedure within a feasible set defined by the relaxed constraints. This feasible set is not restricted within the neighborhood of a given point obtained from the previous iteration. Thus, the proposed method can avoid being trapped in the locally minimum point. Four examples are presented in this paper to demonstrate the effectiveness of the proposed method.      

一种分数阶微分IIR滤波器的设计方法和改进

提出一种在不增加分数阶微分滤波器复杂度的前提下,能有效提高分数阶微分滤波器性能的方法.该方法利用几种基于典型微分算子的分数阶微分滤波器之间的互补性,通过相互内插结合的方式,用于提高IIR分数阶数字滤波器的性能.改进后的分数阶微分滤波器频率响应更接近理想分数阶微分滤波器,表明所提方法的有效性.     

Design of 1-D Stable Variable Fractional Delay IIR Filters

In this brief, a two-stage approach for the design of 1-D stable variable fractional delay infinite-impulse response (IIR) digital filters is proposed. In the first stage, a set of fixed delay stable IIR filters are designed by minimizing a quadratic objective function, which is defined by integrating error criterion with IIR filter stability constraint condition. Then, the final design is determined by fitting each of the fixed delay filter coefficients as a 1-D polynomial. Two design examples are given to show the effectiveness of the proposed design method     

基于MATLAB的IIR数字滤波器的设计

数字滤波器在数字信号处理领域中已经得到广泛应用,MATLAB软件的频谱分析和滤波器的分析设计功能很强,从而使数字信号处理变得十分简单。利用MATLAB的数字滤波器设计工具箱可以快速有效地设计各种数字滤波器,设计简单方便。介绍了IIR数字滤波器的设计原理、步骤以及在MATLAB中的实现。     

精密测距系统中IIR滤波器的设计

文中介绍了精密测距系统中 IIR 滤波器的设计,给出了 IIR 级联滤波器设计的算法流程。并对所设计的滤波器进行了仿真验证,实验结果表明：本文所设计的滤波器,能有效地从调制信号中提取出包络信号。     

基于FGA的IIR数字滤波器的设计与实现

给出了基于FPGA的IIR数字滤波器的设计和实现方法。首先,用双线性变换法设计出巴特沃兹数字带通滤波器的相关参数;其次,利用Maflab软件对所设计的滤波器进行了仿真分析;最后,利用QuartIlsII软件进行了模块设计和功能仿真。实验结果证明了该方法的有效性。     

Design of M‐Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M‐channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop‐band attenuation, which is also taken care of in the proposed algorithm.     

基于Matlab的IIR数字滤波器的设计与实现

提出了一种采用Matlab的数字滤波器设计工具箱FDATOOL快速有效设计IIR数字滤波器的方法,可实时调整滤波器的参数从而使滤波器的设计达到最优。概述了FDATOOL的使用方法,采用DSP Builder建立了实现模型,给出了基于FPGA的IIR数字滤波器的实现流程,并且在最后使用Simulink进行仿真,给出了仿真波形。     

基于Matlab的IIR数字滤波器快速设计

针对数字滤波器的概念比较抽象,且数值计算较为繁琐的问题,文中给出了借助模拟滤波器快速设计IIR数字滤波器的方法,并在Matlab环境下做出了IIR滤波器的快速设计系统。设计实例及运行结果表明,该设计方法简化了IIR数字滤波器的设计程序,并大幅提高了设计效率。     

Automatic Step-size Control in Wave Digital Simulation Using Passive Numerical Integration Methods

Wave digital filter principles can be applied to the numerical solution of many kinds of differential equations. It has been shown that, by merging the wave digital concept with Runge-Kutta methods, algorithms of high accuracy can be found which are passive and hence possess a lot of desirable numerical stability properties.

In this paper, we will discuss the applicability of step-size control within this framework.     

分数导数与数字微分器设计

从信号处理角度来考察分数阶导数和微分问题.首先论述分数阶微积分的基本概念,评论分数阶导数的几种典型定义,并重点探讨分数阶导数的频域定义及其基本性质.紧接着详细研究分数阶微分的实现:理想分数阶数字微分滤波器和FIR分数阶数字微分滤波的基本性质和设计问题,并提出分数阶微分滤波器设计中遇到的新问题以及奇对称微分滤波器、偶对称微分滤波器等新概念.最后给出一些值得进一步探讨的有趣问题.     

基于Matlab的IIR数字滤波器设计方法比较及应用

滤波是信号处理的基础,滤波运算是信号处理中的基本运算,滤波器的设计也就相应成为数字信号处理的最基本问题之一。这里着重IIR数字滤波器的设计研究,应用Butterworth滤波器,ChebysheveⅠ型滤波器,ChebysheveⅡ型滤波器以及椭圆滤波器分别对低通、高通、带通和带阻四种滤波器形式进行比较仿真,通过不同设计方法的对比,将各种滤波器的设计特点很好地呈现出来。应用了Butterworth滤波器实现了混合信号频谱的分离,取得了良好的仿真效果。     

IIR数字滤波器的优化设计和DSP实现

首先叙述了直接Ⅱ型IIR(无限冲击响应)数字滤波器能够克服使用定点DSP实现IIR数字滤波器时引起的输入数据的溢出问题;然后利用MATLAB软件生成滤波器的输入数据和系数,进行相应的数据压缩处理,并生成仿真波形;最后给出了用DSP语言实现直接Ⅱ型结构IIR数字滤波器的完整程序、仿真结果,同时对仿真结果进行了分析、比较。     

利用TMS320C31实现数字滤波

介绍数字信号处理器TMS320C31的硬件结构和指令特点，指出其循环寻址和并行指令系统适合于实现数字滤波，根据无限长单位冲击响应数字滤波器的级联结构，给出了实现该滤波器所需的算法结构，介绍了软件的编写并对此进行了试验。