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.     

高阶Chebyshev低通滤波器的快速设计

Chebyshev滤波器是一种常用的高性能滤波器。本文通过对Chebyshev滤波器的系统函数的推导分解,提出了一种可以快速实现高阶Chebyshev低通滤波器电路的方法,并给出了设计高阶Chebyshev低通滤波器电路的各元器件参数的计算公式。最后运用该算法快速设计了一个7阶Chebyshev低通滤波器,并采用Saber软件对设计的7阶Chebyshev低通滤波器进行了理论分析验证。     

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.     

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.     

基于Matlab的IIR数字滤波器设计

介绍了基于Matlab的IIR数字滤波器设计方法。先确定数字滤波器的性能指标,再按照一定的映射规则（冲激响应不变法或双线性变换法）变换成模拟滤波器的性能指标,然后采用一定的逼近方法（巴特沃斯型或切比雪夫型）设计模拟滤波器,最后将模拟滤波器按照同样的映射规则转变成数字滤波器。同时介绍了设计IIR数字滤波器常用的Matlab函数。通过Matlab实验仿真,利用介绍的数字滤波器的设计方法,成功地设计出了满足预定指标的各型IIR数字滤波器。     

一种新的OTA—电容滤波器信号流图结构

基于传输函数的信号流图模拟,一种新的具有最少元件 Ｏ Ｔ Ａ电容滤波器结构被提出⒚任何种类任何阶电压传输函数均可由该结构实现,设计公式简单⒚文中设计了各种二阶滤波器,分析了这种实现的电压传输函数的灵敏度,给出了三阶椭圆低通滤波器设计实例及计算机仿真结果⒚     

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.     

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.     

Error analysis in fixed-point digital filters using sign-magnitude truncation

The quantization error of a digital filter employing fixed-point arithmetic with sign-magnitude truncation is analyzed. The effect of coefficient quantization is also included. Exact analyses are presented first for Gaussian, sinusoidal and Gaussian plus sinusoidal inputs. Quasi-linearization is then employed to yield a simple computation method of the output noise variance. The resulting expression contains parameters that depend on the input signal statistics. An upper bound is given that is independent of these statistics. Explicit expressions are given for the second-order sections of the digital filter realized in the D1 and D2 forms together with a general expression for the cascade connection of the second-order sections.     

Special functions of circuits and systems

The polynomial solutions of the equation fy″ + gy′ + λy = 0 are obtained and classified for f, g, and λ certain second-degree, first-degree, and zero-degree polynomials, respectively. Applications are given illustrating the use of these polynomials in the construction of amplitude functions and system functions and in tree counting. In particular, all-pole and rational filter functions are considered which include as special cases the Chebyshev, Butterworth, elliptic, Bessel, and various transitional filter functions.     

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.     

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.     

Approximation based on orthogonal and almost orthogonal functions

In this paper, we define a class of almost orthogonal rational functions of Legendre type in a new manner. Relations of these functions with classical exponentional functions orthogonal over interval (0, ∞), as well as classical polynomials orthogonal over (0, 1) are explained. Defining relations of these functions can be used for designing almost orthogonal filters. These filters are generators of orthogonal signals and can be successfully applied in finding the best signal approximation in the sense of the mean square error. The filters orthogonal property enables building of physical (in this case electrical) models of dynamical systems (the sources of signals to be approximated) either with less components for the same model accuracy or higher accuracy for the same number of components than the other known models. New filters represent further improvement of previously designed filters, by the same authors, in the sense of simplicity, higher accuracy, lesser approximation time and even a possibility to approximate signals generated by systems with built-in imperfections. Series of experiments were performed to analyze the dependence of approximation accuracy and the number of filters sections.     

Adaptive event-triggering distributed filter of positive Markovian jump systems based on disturbance observer

This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Reduction of Transfer Functions by the Stability-Equation Method

A method of model reduction for reducing a high-order transfer function to its low-order models is introduced based upon the stability-equation method. The transfer functions of reduced orders are obtained directly from the pole-zero patterns of the stability-equations of the original transfer function. Comparisons with methods in the current literature are made. Extension of the proposed method to discrete systems is given.     

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.     

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.     

基于LabVIEW的虚拟滤波器的设计

随着电子测试技术的不断发展,测试技术正向自动化、智能化、数字化和网络化的方向发展。其中数字滤波器作为测试技术的重要工具而被广泛使用在各个领域。本文设计的滤波器以LabVIEW软件为背景,设计一个能对采集数据波形进行相关处理,并实现相应的参数测量。虚拟滤波器主要包括五个模块:模拟信号的产生、波形的处理、信号的测量、波形的存储与回放、滤波后的波形保存。数据处理模块主要实现数字滤波和加窗函数处理两大功能,可以选择不同的滤波器和窗函数以适应不同的情况,参数的不同设置能够使信号频率不断变化。它是一种测试仪器和系统的概念相结合的软件,结合了测试技术和相应的专业知识。本文介绍了在LabVIEW实现虚拟滤波器测试信号的方法。     

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.     

Fusion estimation for stochastic uncertain systems with time-correlated rician fading channels

In this article, a fusion estimation scheme is proposed for stochastic uncertain systems with time-correlated fading channels (TFCs). A batch of random variables obeying Gaussian distributions is employed to describe the parameter uncertainties. The sensor communicates with the local filter through a TFC where the evolution of the channel coefficient is characterized by a certain dynamic process with one-step correlated noises. For further analyzing the effects of TFCs, a class of additional variables is first introduced by augmenting the dynamics of channel coefficients and the concerned system. Then, a new group of modified local filters is developed and the unbiasedness of local filters is examined by means of inductive method. Furthermore, the filter gains which minimize the local filtering error covariances are designed for the modified local filters in the simultaneous presence of stochastic uncertainties and TFCs. Subsequently, the cross-covariances among local estimates are computed iteratively and, based on the obtained cross-covariances as well as the unbiased local estimates and their corresponding filtering error covariances, a fusion estimate is obtained by using weighted least square fusion method. Finally, the effectiveness of the proposed fusion estimation scheme is verified by two examples.