基于FPGA的IIR数字滤波器的实现

数字信号处理在科学和工程技术许多领域中得到广泛的应用,与FIR数字滤波器相比,IIR数字滤波器可以用较低的阶数获得较高的选择性,本文采用一种基于FPGA的IIR数字滤波器的设计方案,首先分析了IIR数字滤波器的原理及设计方法,然后通过MAX＋PLUSⅡ的设计平台,采用自顶向下的模块化设计思想将整个IIR数字滤波器分为：时序控制、延时、补码乘加和累加4个功能模块。分别对各模块采用VHDL进行描述后,进行了仿真和综合。仿真结果表明,本课题所设计的IIR数字滤波器运算速度较快,系数改变灵活,有较好的参考价值。     

IIR数字滤波器的仿真实现研究

作为改变信号频谱的算法装置,数字滤波器及其设计受到人们广泛地关注,其分为有限长冲激响应（FIR）数字滤波器和无限长冲激响应（IIR）数字滤波器。文中探究具有无限持续时间的冲击响应的IIR数字滤波器系统,并提出如何利用MATLAB软件实现仿真设计。     

Minimax design of two-channel IIR QMF banks with arbitrary groupdelay

The paper deals with the minimax design of two-channel infinite impulse response (IIR) QMF banks with arbitrary group delay, for which the IIR analysis filters and the resulting filter bank possess the frequency response optimal in the minimax (L_∞) sense. Utilising a lattice structure for the denominators of the IIR analysis filters, a design technique is presented based on an approximation scheme and a weighted least-squares (WLS) algorithm, previously developed by one of the authors for solving the resulting design problem that is basically a nonlinear optimisation problem. During the design process, this technique finds the tap coefficients for the numerator and the reflection coefficients for the denominator of the prototype IIR analysis filter simultaneously. The stability of the designed prototype IIR analysis filter is ensured by incorporating an efficient stabilisation procedure to make all of the reflection coefficient values fall between -1 and +1. Computer simulations show the effectiveness of the proposed design technique     

一种有效的IIR数字滤波器优化设计方法

针对IIR数字滤波器优化设计实质上是一个多参数多目标优化问题,本文提出一种基于量子遗传算法的IIR数字滤波器满意优化设计方法,通过设计满意度函数而构造出满意优化计算模型,将滤波器性能指标的满意设计与参数优化统一考虑,并用本文提出的收敛速度快和全局寻优能力强的新量子遗传算法(NQGA)搜索满意解。通过低通和带通IIR数字滤波器的设计结果表明,该方法是有效、实用的。     

PCLS IIR digital filters with simultaneous frequency responsemagnitude and group delay specifications

This paper presents the peak-constrained least-squares (PCLS) approach to designing IIR digital filters. PCLS IIR digital filters that meet simultaneous specifications on the frequency response magnitude and the group delay are introduced. As a point of reference, we consider the IIR digital filter design problem that appears in Deczky's (1972) classic paper and in the popular textbook by Oppenheim and Schafer (1989). In addition, the same design problem appears in the IIR filter design chapter by Higgins and Munson (1993) in the Handbook for Digital Signal Processing. By using our new algorithm with simultaneous optimization of the frequency response magnitude and the group delay, we obtain a dramatic improvement in the solution of this classic IIR digital filter design problem. Starting from the same filter structure and the same specifications for the frequency response magnitude as in the works of Deczky, Oppenheim and Schafer, and Higgins and Munson, we are able to reduce the group delay ripple by a factor of 35. In another design problem that originated in Deczky's work, we use PCLS optimization to reduce the group delay ripple by a factor of 40 at the same time we reduce the stopband energy by 6 dB, without sacrificing any other performance measure. The group delay ripple in this IIR digital filter example is reduced to only ±0.002 samples     

IIR数字滤波器在定点DSP中可实现性的仿真分析

在使用定点DSP芯片实现IIR数字滤波器的工程实践中,对于给定的滤波器设计指标,当取样频率提高时,在Matlab辅助设计中能够实现的IIR滤波器,在TMS320C54x上却特性改变,甚至无法使用。对此进行了较深入的仿真分析和研究,找出了在定点DSP上实现IIR数字滤波器时,滤波器系数取值的约束条件,摸索了解决问题的基本途径。     

An 85-MHz fourth-order programmable IIR digital filter chip

The authors describe the design and VLSI implementation of a single-chip 85-MHz fourth-order infinite impulse response (IIR) digital filter chip fabricated in 0.9-μm CMOS technology. The coefficient and input data word lengths of the filter are 10 b each, and the output data word length is 15 b. The coefficients are fully programmable. The chip can be programmed to implement any IIR filter from first to fourth order or an FIR filter up to 16th order at sample rates up to 85 MHz. A total of seventeen 10×10 multiply-add modules are used in this chip. The chip contains 80000 devices in an active area of 14 mm². It dissipates 2.2 W at 85-MHz clock rate and performs over 1.5×10⁹ multiply-add operations per second. The underlying filtering algorithm, chip architecture, circuit and layout design, speed issues, and test results are described. The results of an E-beam probing experiment on packaged chips at 100-MHz clock rates are also presented and discussed     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L/sub /spl infin// error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.     

Adaptive notch filter design under multiple identical bandwidths

Digital notch filters are applied to remove or suppress the narrow-band interferences in digital signals, while preserving other components unchanged. Under the condition of the identical notch bandwidths, a novel design method is put forward in this paper to realize the adaptive notch filter with infinite-impulse response (IIR). Firstly, a specially simplified all-pass filter is introduced to construct an IIR non-adaptive notch filter, which serves as the core part in the adaptive one. Secondly, the criterion of least-mean-square (LMS) is applied to design the desired adaptive notch filter (ANF). The designed ANF can track and suppress multiple non-harmonic interference components simultaneously. Finally, the effectiveness and practicability of the proposed design method are verified by a set of experimental results.     

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison     

自适应IIR滤波器的遗传算法

基于梯度信息的计算未调节自适应IIR滤波器的系数，需要进行复杂的矩阵运算，计算量大，容易陷入局部收敛．本文构造了稳定性检测十分方便的二阶自适应IIR滤波器的并联结构，并将遗传算法应用到滤波器的系数寻优，可以快速地收敛到全局最优解．     

Digital Filter Design Using Computer Algebra Systems

Digital filter design can be performed very efficiently using modern computer tools. The drawback of the numeric-based tools is that they usually generate a tremendous amount of numeric data, and the user might easily lose insight into the phenomenon being investigated. The computer algebra systems successfully overcome some problems encountered in the traditional numeric-only approach. In this paper, we introduce an original approach to algorithm development and digital filter design using a computer algebra system. The main result of the paper is the development of an algorithm for an infinite impulse response (IIR) filter design that, theoretically, is impossible to be implemented using the traditional approach. We present a step-by-step procedure which includes derivations of closed-form expressions for (1) the transfer functions of the implemented digital filter which contains the algebraic loop; (2) the closed-form expression for computing the number of requested iteration steps; and (3) the error function representing the difference of the output sample values of the new filter and that of the conventional filter. We demonstrate how one can use some already-known multiplierless digital filter as a start-up filter to design a new digital filter whose passband edge frequency can be simply moved by using a single parameter. As a result, we obtain a multiplierless IIR filter, which belongs to the family of low-power digital filters where multipliers are replaced with a small number of adders and shifters.     

Optical half-band filters

This paper proposes two kinds of novel 2×2 circuit configuration for finite-impulse response (FIR) half-band filters. These configurations can be transformed into each other by a symmetric transformation and their power transmittance is identical. The configurations have only about half the elements of conventional FIR lattice-form filters. We derive a design algorithm for achieving desired power transmittance spectra. We also describe 2×2 circuit configurations for infinite-impulse response (IIR) half-band filters. These configurations are designed to realize arbitrary-order IIR half-band filter characteristics by extending the conventional half-band circuit configuration used in millimeter-wave devices. We discuss their filter characteristics and confirm that they have a power half-band property. We demonstrate design examples including FIR maximally flat half-band filters, an FIR Chebyshev half-band filter, and an IIR elliptic half-band filter     

Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

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。     

Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations

The contribution of this paper consists of two individual parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: 1), a given noncausal impulse response is transformed into the first octant using the proposed 3-D invertible mapping technique; 2), the transformed impulse response in the first octant is approximated by balanced model reduction of 3-D separable denominator systems;3), the resultant 3-D IIR filter is transformed back to the original coordinates.     

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。     

基于自适应遗传算法FIR数字滤波器优化设计

FIR数字滤波器优化设计的目标是对滤波器理想性能的逼近。遗传算法是一种模仿生物进化过程的全局优化概率搜索算法,它提出了一种求解复杂系统优化问题的通用框架,且不依赖于问题的领域和种类,在此将自适应的遗传算法应用于FIR数字滤波器的优化设计,通过评价种群的“早熟度”来自适应调整交叉率和变异率,提高了遗传算法的搜索效率。计算机仿真结果证明,该算法能够获得满意的滤波器性能。     

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.