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.     

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.     

A new type of transitional filter based on summation of polynomials

A new transitional filter based on the sum of filter polynomials is proposed and discussed. It shall be shown that the approach allows for greater flexibility in adjusting passband and stopband gain shapes. The sensitivity of the filter transfer function is analyzed and related to the approximation problem. Some new modified classical filters are also derived including maximally flat (Butterworth) and equiripple (Chebyshev) types. Several examples of combining Butterworth, Chebyshev and sync-tuned filters are presented and compared to those obtained using the conventional product method. The new transitional filter provides an alternative to other forms and provides a means for isolating the effects of non-uniformly distributed pole angles.     

Analytical design of multidimensional recursive digital filters with cubic symmetry and constant group delays

An analytical technique is developed for designing multidimensional (M-D) separable-denominator recursive digital filters that meet, simultaneously, magnitude and phase specifications. A cubic symmetry that exists in the M-D frequency response is incorporated into the M-D filter structure. The denominator and the numerator of an M-D transfer function are designed separately. The former is used to approximate constant group delays and the latter is used to adjust an overall magnitude response. The filter is analytically designed by solving linear equations only. This serves to reduce the amount of calculations drastically. The stability of the resulting filter is always guaranteed. Finally, two examples are given to illustrate the utility of the proposed technique.     

Realizability-Preserving Transformations for Digital and Analog Filters

The theoretical basis for the design of analog and digital filters by prototype and transformation is studied. Necessary and sufficient conditions are developed for a transformation to preserve realizibility as well as the frequency response. The attendant structural properties of such transformations are developed and compared with the reactance transformations of classical analog filter theory. The superiority of direct analog-to-digital transformation to the Constantinides approach is proven.     

System functions for 2D linear phase frequency sampling filters

In this paper, four frequency sampling filter system functions which are classified as Type 1-1, Type 1-2, Type 2-1 and Type 2-2, are developed. Each type of these frequency sampling filter interpolates a frequency response through a specific set of frequency samples and also uses these frequency samples as coefficients in each of their implementations. Each of these system functions are further developed for 2D linear phase filters that have real impulse responses and for 2D linear phase filters that have real impulse responses and fourfold symmetry. The approximate conditions for which these frequency sampling filters can implement narrowband 2D linear phase filters and narrowband 2D linear phase filters with fourfold symmetry more efficiently than direct convolution filters are also derived.     

TUT and TABU transitional filters

Transitional XY filters (TXY) are considered with characteristics that vary smoothly from those of filter X to those of filter Y as a parameter is varied continuously. Emphasis is placed on transitional ultraspherical—Thomson (TUT) filters and transitional ultraspherical “a”-ultraspherical “b” (TABU) filters.     

Parasitic tolerant designs of sampled data filters using switched capacitors and unity gain amplifiers

New and systematic procedures are presented for realizing sampled data filter (SDF) functions using switched capacitors (SCs) and unity gain amplifiers (UGAs). The procedures are attractive and simple to implement. Any SDF, recursive or non-recursive and of any order, can be realized using the methods presented. The designs of biquadratic SDFs is discussed in detail. The resulting realizations possess the property that the numerator and denominator coefficients of the SDF functions can be controlled by independent capacitance ratios. This makes the filters attractive for adaptive applications. The sensitivity properties of the resulting filters are analyzed and guidelines given for obtaining low sensitivity realizations. A method is also suggested to make the filters relatively insensitive to the parasitic capacitances in the circuit. Finally, a step by step procedure, easily implemented in a computer, is given. Starting from the given analog filter specifications, the method yields a design that has very low sensitivity, uses minimum total capacitance and is tolerant of the various parasitic capacitances in the circuit. Experimental results show very good agreement with the theoretical analysis.     

l1 filtering for continuous-discrete T-S fuzzy positive Roesser model

This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l₁ performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l₁-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.     

A new design method based on artificial bee colony algorithm for digital IIR filters

Digital filters can be broadly classified into two groups: recursive (infinite impulse response (IIR)) and non-recursive (finite impulse response (FIR)). An IIR filter can provide a much better performance than the FIR filter having the same number of coefficients. However, IIR filters might have a multi-modal error surface. Therefore, a reliable design method proposed for IIR filters must be based on a global search procedure. Artificial bee colony (ABC) algorithm has been recently introduced for global optimization. The ABC algorithm simulating the intelligent foraging behaviour of honey bee swarm is a simple, robust, and very flexible algorithm. In this work, a new method based on ABC algorithm for designing digital IIR filters is described and its performance is compared with that of a conventional optimization algorithm (LSQ-nonlin) and particle swarm optimization (PSO) algorithm.     

Distributed delay input shaper design by optimizing smooth kernel functions

The aim of this paper is the development of a general class of input shapers with distributed time delay which leads to retarded spectral properties. The design of the shaper is formulated as a multi-objective optimization problem, where response time and robustness, expressed in terms of residual vibrations, are the main objectives. As a part of the optimization formulation, common requirements for input shapers such as non-decreasing step response and unity steady state gain are considered in the design. Moreover, additional optional requirements, such as smoothness of a step response, jerk and even jounce limits can be added to optimization procedure. The resulting problem can be solved using convex optimization techniques. Several illustrative examples are presented in comparison with classical input shaping techniques. Finally, implementation aspects are discussed. The paper is accompanied by an implementation in MATLAB, including a user-friendly interface for the interactive shaper design.     

A simple form synthesis of linear time-variant digital filter via spectral decomposition of its impulse response

The paper describes a new technique to synthesize a finite impulse response of linear time-variant (LTV) digital filter. First, a finite impulse response is decomposed into a sum of products of two orthogonal sequences. The direct implementation of the decomposed impulse response leads to the parallel connection of linear time-invariant (LTI) digital filters, followed by time-varying multipliers. A simple filter structure is obtained by properly modifying the sequences to realize the parallel form structure as a cascade connection of first- or second-order recursive LTI filters. The structure is easy to implement on a computer and saves computation time. Numerical examples illustrating the technique are included.     

A class of fast and accurate deterministic trend decomposition in the spectral domain using simple and sharp diffusive filters

This study proposes a spectral domain algorithm to remove the deterministic non-periodic trend from a time series using a class of fast, sharp and diffusive filters. These filters are principally the iterative moving least squares methods weighted using Gaussian windows. The responses of the filters expressed in analytic forms are proven to be diffusive. If it is a polynomial of finite degree, the embedded trend can be decoupled by the filters with specific order and iteration steps. The filters’ order, transition zone, error tolerance, iteration number and smoothing factor are subject to two algebraic equations to form a specific class. The operation counts of all filters are slightly larger than twice that applying a Fast Fourier Transform (FFT). It is numerically shown for a given transition zone and tolerance, there is a filter generating the shortest error penetration distance among all the filters. If either the trend or a spectral band is the main concern, there is an optimal strategy to shrink the error penetration distance. The numerical results show the filter has better performance than several existing methods. In addition, four examples successfully show direct applications of the filter’s response.     

Frequency synchronization for interleaved OFDMA uplink systems

This study presents a novel frequency synchronization scheme for orthogonal frequency division multiple access uplink systems. The proposed approach first estimates the carrier frequency offset (CFO) from the zeros of a backward prediction system. Then, based on the CFO estimates, two types of filters, namely zero-forcing and the linearly constrained minimum variance filters, are developed to suppress multiple access interference (MAI). Computer simulation results show that in addition to having a reduced computational complexity, the proposed algorithm has reliable CFO estimates and possesses at least a 3-dB power gain in MAI suppression over conventional minimum mean square error algorithms for frequency synchronization.     

适用于海事卫星终端的体声波滤波器设计

近年来,国际海事卫星应用范围的扩展对终端设备的微型化与抗噪性提出了更高的要求,薄膜体声波滤波器成为人们关注的焦点。相对于传统滤波器,体声波滤波器具有更高的谐振频率和温度稳定性,更低的损耗和成本,同时可以实现芯片集成。本文介绍了FBAR体声波滤波器的工作原理与设计模型,在此基础上设计出了适用于BGAN下行频段的窄带滤波器。为实现材料参数的实时调整,本文采用Mason模型,通过改变串并联单元级数与面积比,最终设计出滤波器频带为1525~1559Mhz,带外抑制60dB,插损4.3dB。     

A computer-oriented approach to obtaining an analytical expression of an impulse response of a one- or two-dimensional filter

A method is presented, that can be readily written in a computer program, to obtain the closed-form solution of the impulse response of a digital filter. The extension of this approach to two-dimensional digital filters and to analog filter transfer functions is also presented. Examples are shown.     

基于陪审团机制的垃圾邮件过滤系统

目前对垃圾邮件的过滤主要有基于内容、基于IP地址和基于规则等方法,这些方法对垃圾邮件的过滤起到了一定作用。但单种邮件过滤技术只是针对邮件的某种属性进行过滤,因而造成邮件过滤判断的片面性。对此,设计了基于陪审团机制的邮件过滤系统。在这个系统中,各种现有的邮件过滤器对邮件的过滤结果,并非邮件过滤的最后结果,而是作为该系统的邮件过滤判断的一个输入值,最后根据系统所定的计算规则得出邮件的最终过滤结果。     

Finite-time command filter-based adaptive fuzzy tracking control for stochastic nonlinear induction motors systems with unknown backlash-like hysteresis

In this article, an adaptive fuzzy control method is proposed for induction motors (IMs) drive systems with unknown backlash-like hysteresis. First, the stochastic nonlinear functions existed in the IMs drive systems are resolved by invoking fuzzy logic systems. Then, a finite-time command filter technique is exploited to overcome the obstacle of “explosion of complexity” emerged in the classical backstepping procedure during the controller design process. Meanwhile, the effect of the filter errors generated by command filters is decreased by utilizing corresponding error compensating mechanism. To cope with the influence of backlash-like hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. The finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the stochastic disturbance and backlash-like hysteresis are considered to improve control accuracy. It’s shown that the tracking error can converge to a small neighborhood around the origin in finite-time under the constructed controller. Finally, the availability of the presented approach is validated through simulation results.     

Conditionally bilinear filter with tracking application

A recursive nonlinear filter and tracking methodology is developed here for a class of partially observable processes. The method is based on an approximation of a nonlinear system by a system which is linear in the unobservable states and has the unobservables conditionally Gaussian with respect to the observations initially. Model smoothness, such as required with most approximating filters is not required here, and applications to simulated tracking problems show the filter to be considerably more accurate than the modified second-order filter which in general sense includes the extended Kalman filter.     

Output feedback exponential stabilization of uncertain chained systems

This paper deals with chained form systems with strongly nonlinear disturbances and drift terms. The objective is to design robust nonlinear output feedback laws such that the closed-loop systems are globally exponentially stable. The systematic strategy combines the input-state-scaling technique with the so-called backstepping procedure. A dynamic output feedback controller for general case of uncertain chained system is developed with a filter of observer gain. Furthermore, two special cases are considered which do not use the observer gain filter. In particular, a switching control strategy is employed to get around the smooth stabilization issue (difficulty) associated with nonholonomic systems when the initial state of system is known.