Nomographs and filters

This paper presents the nomographs for additional classical filters, including ultraspherical, Legendre, modified associated Legendre, Papoulis, Halpern, Bessel, Gaussian, and synchronously-turned. It also identifies inaccuracies in the earlier nomographs. The basic theory of nomographs and their utilization in developing filter nomographs is presented.     

Optimum non-linear Wiener filters

General conditions are given for the optimality of non-linear Wiener filters which minimize the mean-square difference between the desired and actual filter outputs. These conditions, which are a generalization of the Wiener–Hopf equation are applied to the Gaussian case and the kernels of the optimum realizable and unrealizable systems are derived.     

Transient responses of m-derived filters

The analytic expressions of the unit-impulse and the unit-step responses ofthe classical m-derived and the composite filters are derived. The equations have been computed by means of an IBM 360 Model 44 digital computer. Normalized curves of the unit-step response are presented. They are completely universal and can be applied to specific situations by rescaling the axes.     

Selectivity nomographs for classical filters

Nomographs for determining the filter order of classical filters based on selectivity requirements are presented. The selectivities for a variety of standard classical filters are summarized in equation form and the general selectivity nomograph is constructed. The selectivity equations are then converted into nomograph form by applying the relationship between the transfer function and the response slope. Design examples are presented to demonstrate the usefulness of the selectivity nomographs. These nomographs can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.     

On the construction of transitional filter nomographs

The construction of nomographs for transitional classical filters is described. Gain functions of classical filters are related to filter requirements resulting in a formulation for the general gain nomograph. The transitional filters that are products of approximating polynomials are incorporated into the general gain nomograph resulting in transitional filter nomographs that are sums of the individual nomographs. Nomographs for transitional filters using alternative forms where poles are interpolated are also considered. The resulting nomographs allow for quick optimization of transitional filter frequency response in many cases. Design examples are submitted and discussed. The proposed transitional filter nomographs provide the engineer with increased insight into the selection of classical transitional filters with optimum frequency response.     

Rational approximation of three-dimensional digital filters

Two techniques are developed for approximating a given three-dimensional (3-D) digital filter by a 3-D rational function. The one is by a general 3-D rational function and the other by a 3-D rational function which is separable in the denominator. Each technique relies on the use of mixed first and second information, in the form of a finite portion of the impulse response and its autocorrelation sequence. The approximation is performed by solving a set of linear equations. The separable-denominator approximation is more advantageous due to the guaranteed stability and reduced amount of calculations.     

Block implementation of two-dimensional digital filters

A novel principle known as block transformation is developed for the block implementation of two-dimensional (2-D) digital filters. It employs the one-dimensional (1-D) block implementation concept forwarded by Burrus (7) as a basic tool. Using this block transformation principle three distinct forms of 2-D block equations are derived. The generalized nature of the approach presented here facilitates the straightforward extension of this technique to higher dimensional digital filters.     

A special class of multiplierless digital filters

This paper deals with the design of discrete low-pass filters, using a special class of polynomials of the second and third order, with coefficients which are powers of two. To take advantage of the characteristics of these polynomials, the discrete integrator is used as a basic component. The filters so derived are multiplierless resulting in hardware economy. Simulation indicates that the filters obtained are equally good or better than those obtained by the application of the impulse invariance method.     

Event-triggered optimal and suboptimal distributed Kalman consensus filters for sensor networks

This paper studies the distributed Kalman consensus filtering problem based on the event-triggered (ET) protocol for linear discrete time-varying systems with multiple sensors. The ET strategy of the send-on-delta rule is employed to adjust the communication rate during data transmission. Two series of Bernoulli random variables are introduced to represent the ET schedules between a sensor and an estimator, and between an estimator and its neighbor estimators. An optimal distributed filter with a given recursive structure in the linear unbiased minimum variance criterion is derived, where solution of cross-covariance matrix (CCM) between any two estimators increases the complexity of the algorithm. In order to avert CCM, a suboptimal ET Kalman consensus filter is also presented, where the filter gain and the consensus gain are solved by minimizing an upper bound of filtering error covariance. Boundedness of the proposed suboptimal filter is analyzed based on a Lyapunov function. A numerical simulation verifies the effectiveness of the proposed algorithms.     

Large signal-performance of active filters using amplifier pole

The effect of operational-amplifier nonlinearity on the performance of active-R, active-C, and “partial” active-R filters is investigated. Theoritical and experimental results show that the amplifier slew-rate limitation results in a characteristic which slants from the ideal flat response of the filter transfer functions.     

Iterated gain-based stochastic filters for dynamic system identification

We propose a novel form of nonlinear stochastic filtering based on an iterative evaluation of a Kalman-like gain matrix computed within a Monte Carlo scheme as suggested by the form of the parent equation of nonlinear filtering (Kushner–Stratonovich equation) and retains the simplicity of implementation of an ensemble Kalman filter (EnKF). The numerical results, presently obtained via EnKF-like simulations with or without a reduced-rank unscented transformation, clearly indicate remarkably superior filter convergence and accuracy vis-à-vis most available filtering schemes and eminent applicability of the methods to higher dimensional dynamic system identification problems of engineering interest.     

Design of switched-capacitor filters using non-ideal op amps

A general synthesis procedure is given for the realization of switched-capacitor filters in the z-domain. The method uses biphased switches, capacitors and non-ideal op amps with finite gain-bandwidth product. The design includes at the outset the effects of the op amp gain-bandwidth product. Two examples are given which have been verified by a computer program.     

Frequency limitations of active-R filters using operational amplifiers

Active-R filters are designed using internally compensated operational amplifiers (OA) and resistors only. A one-pole or 6 dB roll off model for the PA's is assumed in these designs. This model is adequate for active-RC filters. However, for active-R filters such an assumption leads to serious accuracy as well as stability problems, thereby limiting the highest operating frequency of these filters to well below their potential maximum. It is shown in this article that a two-pole or 12 dB roll off model more accurately reflects the behaviour of the OA's for the above active-R realizations. A quantitative measure of the limitation imposed by this model on such realizations is also presented. Extensive computer simulation and experimental tests have been carried out that verify closely the theoretical predictions.     

我国宏观经济转型的微观诠释——企业战略变化

基于我国宏观经济转型带动的企业战略变化的客观性、普遍性和持续性,对经济转型初期、中期、后期我国企业战略变化在形式、内容、过程等方面的特点进行了比较性归纳,并对我国企业战略变化行为相对成熟的市场经济背景下企业战略变化行为的特殊性、存在的主要问题进行了分析,最后指出了未来战略变化问题的研究方向.     

Least-squares design of two-dimensional recursive filters with specified magnitude and linear phase

An efficient space-domain procedure is presented for the design of two-dimensional recursive filters with specified magnitude and linear phase. The design procedure is based on both the canonical and the modified least-squares approximation techniques. The nonlinear equations obtained in the canonical least-squares approximation are efficiently solved by the one- dimensional Gauss—Newton optimization method, after the two-dimensional data are lexico- graphically ordered. The gradient and the Hessian matrix, needed in the solution, are calculated recursively. Initial values of the parameters are obtained from the linear modified least-squares (MLS) approximation. To illustrate the efficiency of the proposed design procedure, the design of fan and circularly symmetric filters are given.