Closed-Form Design of Digital IIR Integrators Using Numerical Integration Rules and Fractional Sample Delays

In this paper, the numerical integration rules and fractional sample delays will be used to obtain the closed-form design of infinite-impulse response (IIR) digital integrators. There are two types of numerical integration rules to be investigated. One is Newton-Cotes quadrature rule, the other is Gauss-Legendre integration rule. Although the proposed IIR digital integrators will involve the implementation of fractional sample delays, this problem is easily solved by applying well-documented design techniques of the finite-impulse response Lagrange and IIR allpass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method     

Digital integrator design using Simpson rule and fractional delay filter

The IIR digital integrator is designed by using the Simpson integration rule and fractional delay filter. To improve the design accuracy of a conventional Simpson IIR integrator at high frequency, the sampling interval is reduced from T to 0.5T. As a result, a fractional delay filter needed to be designed in the proposed Simpson integrator. However, this problem can be solved easily by applying well-documented design techniques of the FIR and all-pass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method.     

Design of digital FIR variable fractional order integrator and differentiator

This paper presents an easy and simple method to design variable fractional order digital FIR integrators and differentiators based on fractional order systems. First, closed-form digital IIR fractional order integrators and differentiators have been obtained from the analog rational functions approximations, in a given frequency band, of the fractional order integrator s ^?m and differentiator s ^m (0?<?m?<?1) through the Tustin generating function. Then, closed-form digital FIR fractional order integrators and differentiators by truncation of the digital IIR ones have been derived. Next, polynomial interpolation has been used to design digital FIR variable fractional order integrators and differentiators that can be implemented by the Farrow structure. The main feature of variable fractional order operator is that its order can be changed without re-designing a new fractional order operator. Some examples have been presented through the paper to illustrate the performance and the effectiveness of the proposed design method. The results obtained have been discussed and have been compared to one of the most recent works in the literature using the same design parameters.     

High-Order Passive Delay-Based Macromodel for MTLs via Symplectic Integrators

This letter introduces a new approach to obtain passive delay-based macromodels for lossy multiconductor transmission lines. The proposed approach uses the notion of symplectic integrators to obtain fourth-order passive approximations to the exponential matrix with delay extraction. This approach can therefore be considered a generalization to previous delay-extraction-based techniques which adopt second-order approximations to the exponential function.     

移动运营商需要新一代应用集成合作伙伴

随着中国移动通信的迅猛发展，运营商的业务支撑系统将面临机遇和挑战；满足用户数的不断增长，紧跟移动通信技术和互联技术的发展，遵循统一的技术规范，积极参与加入WTO后的市场竞争。另一方面，承担运营商业务支撑系统建设和完善的移动应用集成商，也应在软件产品、应用解决方案和应用集成等方面，不断提升和创新，向运营商提供全方位的服务支持和全优的工程管理。     

GaAs FET Current-Mode Integrators and Their Application to Filters

In this paper, current-mode integrators which consist of only n-channel depletion-mode FET and their application to filters are presented. Lossy integrator is simply realized with a capacitor and a grounded gate FET. Lossless integrator can be obtained by providing a lossy integrator with a positive feedback. To do this, multi-output current mirror is proposed. To reduce 2nd-order harmonic and THD of the filter, unbalanced/balanced conversion circuit is proposed. As an application example, 3rd-order leapfrog low-pass Chebyshev filter is simulated with GaAs MESFET process parameters. Simulation results show good performances.     

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     

Low-Voltage High-Frequency Continuous-Time Filters Based on Simple Transconductors and Miller Integrators

An approach to implement low-voltage continuous-time filters using simple transconductance elements and gain-stage Miller integrators is presented. The technique allows direct translation of an RC active structure or a system block diagram into a CMOS circuit that uses differential pairs as transconductors and gain stages as Miller Integrators. A novel and efficient compensation technique to cancell excess phase in Miller integrators is discussed. A new high-frequency compensated CMOS universal filter structure that has no summing nodes in the main feedback loop is discussed and experimentally verified.     

Using fractional delay to control the magnitudes and phases of integrators and differentiators

The use of fractional delay to control the magnitudes and phases of integrators and differentiators has been addressed. Integrators and differentiators are the basic building blocks of many systems. Often applications in controls, wave-shaping, oscillators and communications require a constant 90deg phase for differentiators and -90deg phase for integrators. When the design neglects the phase, a phase equaliser is often needed to compensate for the phase error or a phase lock loop should be added. Applications to the first-order, Al-Alaoui integrator and differentiator are presented. A fractional delay is added to the integrator leading to an almost constant phase response of -90deg. Doubling the sampling rate improves the magnitude response. Combining the two actions improves both the magnitude and phase responses. The same approach is applied to the differentiator, with a fractional sample advance leading to an almost constant phase response of 90deg. The advance is, in fact, realised as the ratio of two delays. Filters approximating the fractional delay, the finite impulse response (FIR) Lagrange interpolator filters and the Thiran allpass infinite impulse response (IIR) filters are employed. Additionally, a new hybrid filter, a combination of the FIR Lagrange interpolator filter and the Thiran allpass IIR filter, is proposed. Methods to reduce the approximation error are discussed.     

差分式CMOS连续时间电流模式滤波器

提出了基地电流镜电路的差分式连续时间电流模式积分器，并用此积分器构成了全差分式连续时间电流模式低通及带通滤波器，分析并模拟了所提出的积分器及滤波器的特性，结果表明所提出了电路的具有结构简单，对称性好，失真小等优点，适于全集成。     

Assessment method of numerical integration used in measuring profile based on ultra-precise thin light beam scanning

In order to improve the precision of profile measurement based on ultra-precise thin light beam scanning, an assessment method that compares different numerical integration algorithms in frequency-domain is put forward. The compared numerical integration methods are regarded as recursive digital filters. Through comparing their functions of frequency response in frequency-domain, the delivering role of noise with different frequencies can be analyzed directly and clearly in the process of integrating measured slope data. Analyzing results show that the method of cubic spline is better than trapezoidal, Simpson and 3/8 Simpson rules.     

开关电容积分器的瞬态行为模型

对电路进行行为级模拟的关键是建立电子子模块的行为模型，用以描述电路模块的功能以及电路非理想效应的影响。本文采用瞬态分析方法，建立了基本模拟单元电路开关电容积分 的行为模型。由于对积分器中的运算放大器采用了单极点跨导运放模型，考虑了其有限增益、带宽、转换速率和输出阻抗的影响，提高了开关电容积分器行为模型的精度。电路模拟的结果表明，模型的误差在３％以内。     

A novel SFG structure for C-T high-pass filters

A signal flow graph (SFG) structure for simulating passive high-pass ladder filters, called the incremental integration structure, is proposed. The structure requires the use of integrators with nonintegrating inputs, and an implementation based on the MOSFET-C technique is discussed. The incremental integration structure is compared to the leapfrog and direct SFG simulation structures. Leapfrog high-pass filters are relatively simple and show good noise properties, but they are based on differentiators and thus stability problems exist. The direct SFG simulation method is based on integrators and has good stability properties, but it leads to a relatively high circuit complexity and a high noise level. However, the incremental integration structure inherits the low-noise properties of the leapfrog structure and the good stability of the direct SFG simulation method. A sixth-order elliptic high-pass filter chip with a passband frequency of 3.0 kHz has been manufactured, and measurements support the validity of the approach     

太阳模拟器中长方形光学积分器的应用与研究

针对要求辐照面为长方形的太阳模拟器提出和应用了长方形光学积分器,并对这种太阳模拟器的光学积分器系统进行了详细的阐述,给出了不同长宽比情况下,元素透镜的宽度归一化后元素透镜的分布和数目表格,为以后长方形辐照面的太阳模拟器光学系统设计提供了参考.     

An automatic procedure for the synthesis and optimization of very low-frequency Gm–C integrators

Fully integrated low frequency filters are critical cells that should be carefully designed in order to avoid excessive area occupation. In this work we propose an automatic procedure capable of optimizing the design of G_m?CC integrators, which constitute the basis of a wide class of G_m?CC filters. The optimization target is minimizing the cell area with constraints on input range and low frequency noise. Lower and upper bounds can be fixed to most quantities and design parameters in order to avoid solutions that are not compatible with the physical limitations of the process. The program has been developed within the MATLAB^? platform, exploiting the optimization toolbox. The effect of several important design parameters on the optimization of low frequency integrators has been investigated using the proposed routine. The strong interaction between noise and low frequency constraints has been demonstrated, showing the impressive impact of strict noise specifications on the occupied area. The actual effectiveness of parameters such as the current division factor or approaches such as flicker noise rejection by means of chopper modulation has been investigated. Examples of integrator synthesis, performed using the proposed procedure configured with the parameters of a commercial CMOS process, are presented. The consistence between the characteristics of the cells and the initial specifications has been checked using electrical simulations showing a maximum discrepancy with the initial specifications of nearly 80%. A semi-manual method to refine the synthesized cells and improve the accuracy is proposed.     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

A new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control systems

Infinite impulse response filters have not been used extensively in active noise and vibration control applications. The problems are mainly due to the multimodal error surface and instability of adaptive IIR filters used in such applications. Considering these, in this paper a new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control applications is proposed. At first an RLS-based adaptive IIR filter with computational complexity of order O(n²) is derived, and a sufficient condition for its stability is proposed by applying passivity theorem on the equivalent feedback representation of this adaptive algorithm. In the second step, to reduce the computational complexity of the algorithm to the order of O(n) as well as to improve its numerical stability, a fast array implementation of this adaptive IIR filter is derived. This is accomplished by extending the existing results of fast-array implementation of adaptive FIR filters to adaptive IIR filters. Comparison of the performance of the fast-array algorithm with that of Erikson’s FuLMS and SHARF algorithms confirms that the proposed algorithm has faster convergence rate and ability to reach a lower minimum mean square error which is of great importance in active noise and vibration control applications.     

基于对数域无损积分器的高阶滤波器设计

提出利用双极型晶体管构成的对数域无损积分器以及对数压缩和指数扩展电路实现高阶滤波器.基于无源网络模拟,该设计不仅方法简单,而且使用元件种类很少,易于集成给出一个6阶Butterworth带通滤波器设计实例.PSpice仿真结果表明,该对数域滤波器能在低电压条件下工作,并具有高频、宽调谐范围和低失真等特性.