A New Approach for Filtering and Derivative Estimation of Noisy Signals

Filtering and estimation of derivatives in a single step from noisy signals is an important and challenging task in signal processing. The aim of this paper is to propose a new tracking differentiator based on only one parameter; this differentiator is able to synchronously filter noise and estimate the derivative of the input signal. The new tracking differentiator design is based on an inverse Taylor series approach. Both error and stability analyses of the tracking differentiator design are provided. Theoretical analysis and computer simulation results show that this tracking differentiator cannot only obtain better filtering results than previous approaches but can also estimate the derivatives with high accuracy.     

Frequency and Offset Online Estimation of Sinusoidal Signals Based on High-Order Nonlinear Continuous Differentiator

Real-time parameter identification of si-nusoidal signals is an essential research topic due to its broad utilization in both theoretical studies and engineer-ing practice. A tracking differentiator based online estima-tion framework has been proposed to simultaneously iden-tify frequencies and offset of given multi-sinusoidal signal. Tracking differentiator is exploited in presented framework to track the time derivatives of measurements which are then utilized to estimate the frequencies and offset. We introduce a tracking differentiator called high-order non-linear continuous differentiator into the framework, giving birth to a new estimation algorithm. Comparative exper-iments on both single and two sinusoidal signal are sim-ulated, indicating the superiority of proposed method on both convergent speed and estimation accuracy.     

跟踪微分器在半捷联导引头中的应用

对半捷联稳定方式导引头进行了研究,导出了半捷联导引头稳定控制原理,并进一步建立了完整的半捷联导引头稳定回路框图。介绍了跟踪微分器的工作原理,并对其进行了数值仿真,仿真结果显示了跟踪微分器良好的跟踪性能和滤波性能。在半捷联稳定中,为了减小由框架角位置微分求取框架角速度引入的较大的测速噪声,提出了采用跟踪微分器的方法。数值仿真和半实物实验结果说明了跟踪微分器能有效地从角位置信号中微分求得角速度信号,系统稳定精度提高了80%,证明了跟踪微分器在半捷联稳定中应用的可行性和有效性。     

一种基于IQP的稳定IIR微分器设计新算法

在分析基于常规QP方法来设计稳定IIR微分器而存在的苛刻的稳定性约束和代价函数不可靠两点不足的基础上，本文提出了一种新的基于IQP的稳定IIR微分器设计算法，本算法应用Rouche定理和有关的收敛准则，解决了稳定性和代价函数存在的问题，从而有效地减少了微分器的设计误差，改善了微分器的性能，使得新的设计方法更加完善、可靠。实例证明了这种设计方法的合理性、可行性，从而为它更加宽广的应用前景奠定了基础。     

A second-order microwave differentiator

A novel approach consisting of discrete signal processing (DSP) technique and optimization method is developed to implement a second-order differentiator at microwave frequencies. To utilize the transfer function of a second-order differentiator developed in the DSP study, we formulate the chain scattering parameters of transmission lines in the Z domain. In particular, it is shown that shunt stubs combining with nonuniform serial lines lead to the realization of a second-order microwave differentiator. Some examples are presented to illustrate the validity of this approach.     

有源微分电路设计

用理想运放模型设计的有源微分电路的不足表现为，幅频特性有远离微分规律的尖峰，符合微分规律的频带不宽。为此提出在有源微分电路的传递函数中计及实际运放幅频特性，增加与输入电容串联的电阻，可使有源微分电路的幅频特性没有不符合微分规律的尖峰，符合微分规律的频带达到最宽。     

New grounded-capacitor ideal differentiators

A general scheme is presented in which a grounded-capacitor ideal integrator (GCII) function is reciprocated to realize a grounded-capacitor ideal differentiator (GCID) function and vice versa. Some new single-amplifier grounded-capacitor ideal differentiator structures are also reported.     

On distributed order integrator/differentiator

In this paper, we derive the impulse response of the distributed order integrator/differentiator and its asymptotic property by using the complex path integral. Based on the derived analytical impulse response, we present a technique to perform the discretization of the above distributed order integrator/differentiator. The derived asymptotic property can be applied to verify the feasibility of this method. Some new features of the distributed order integrator/differentiator are shown in time and frequency domains. A number of illustrated figures are presented to validate the concepts.     

Novel approach to designing digital differentiators

A novel approach to designing recursive stable digital differentiators is introduced. A four-step design procedure is presented. The procedure consists of obtaining or designing an integrator and then modifying its transfer function appropriately to obtain a stable differentiator. As an example a second order recursive differentiator is developed.<>     

Multifunction active RC circuit with grounded capacitors

A new active RC circuit with grounded capacitors is proposed, which can perform as any one of the following devices: noninverting differentiator, inverting differentiator, capacitance bridge, inductance simulator, bandpass filter and oscillator.     

Ultra-low voltage fractional-order differentiator and integrator topologies: an application for handling noisy ECGs

Fractional-order differentiator and integrator topologies are introduced in this paper. They offer the benefits of resistorless realizations, electronic adjustment of their characteristics, and capability for operating in 0.5 V power supply voltage. These have been achieved through the employment of the concept of the Sinh-Domain filtering. The performance of the proposed blocks has been evaluated through the Analog Design Environment of the Cadence software, using MOS transistor models provided by the TSMC 180 nm process. As application example, the design of a Sinh-Domain chain for realizing the preprocessing of the Pan-Tomkins algorithm has been given, where the conventional differentiator has been substituted by a fractional-order differentiator.     

A Square-Root Domain Differentiator Circuit

Companding circuits are very useful blocks for realizing low-voltage, high-frequency analog systems. They are implemented using the translinear principle and the quadratic/exponential I-V characteristic of MOS/BJT transistor. In this paper, a Square-Root Domain differentiator is proposed. It is constructed from an appropriate input stage that converts the input current into a compressed voltage at a capacitor's node, and simultaneously senses the capacitor's current. The overall configuration of the differentiator also includes a current geometric-mean circuit and a multiplier, both based on a translinear loop. An attractive characteristic of the proposed circuits is their immunity to body effect. HSPICE simulation results were used for evaluating the behaviour of the differentiator.     

Nonlinear FIR differentiator for quantised input signals

The proposed nonlinear finite impulse response (FIR) differentiator is optimised for the reduction of quantisation error when processing signals of constant or slowly varying rate. Judicious use of a number theoretic approach to rate estimation for some input sequences reduces mean-squared error, relative to that of the optimum linear differentiator, whilst facilitating simple implementation.     

Image-motion detection using analog VLSI

Motion detection by differentiating the output currents of photosensors arranged in a 2D array is described. Subnanoampere current differentiation is made possible by the use of a novel current-mirror (CM) differentiator that requires only four MOSFETs. The pixel density of the motion-detecting imager is higher than 40 pixels/mm². Experimental results of the CM differentiator are reported     

FIR differentiators for quantized signals

The impact of quantization noise on a signal whose rate is to be estimated using a FIR differentiator is analyzed, concentrating on the important constant-rate case in order that the filter be optimized for systems with low-frequency rates of change. Formulae for the mean-squared error of the filter, the corresponding spectral characteristics, and general formulae governing the filter coefficients are derived. The characteristics of four specific differentiators, including a representative wideband differentiator, are examined and compared. It is shown that a differentiator that is optimum in terms of its attenuation of white noise can also be considered optimum with respect to quantization noise attenuation in certain circumstances. An elegant relationship is derived between worst-case RMS error and the fractional value of the rate at which this error occurs. Minimization of this worst-case mean-squared error is shown to be achieved with a simple differentiator. However, the corresponding average error is poor, and a simple nonlinear filter that minimizes the worst-ease error, while retaining a similar average mean-squared error to that of the “optimum” differentiator, is proposed. The equivalence between FIR differentiators and the decoders used in single-loop sigma-delta modulators is also highlighted     

An Effective Approach to Finding Differentiator Window Functions Based on Sinc Sum Function

An approach to finding digital differentiator window functions is studied. The frequency response of the truncated ideal differentiator is expressed by two parts. One is the ideal frequency response and the other is the deviation on the interval from ω=0 to ω=π. The deviation expression is the sum of weighted functions, where the general expression of these functions is equal to the half-sum of a pair of sinc sum functions plus π, and each weight is a window constant. Using the properties of the sinc sum function eight properties of the general expression and six properties of the deviation expression are deduced. By these properties both the relative errors of the passband and the change of their ripples can be small if each weight is proper and the truncated ideal differentiator is ideal at ω=0. From the expression of the deviation a matrix equation with window constants as unknowns can be written. Examples are given about how to write the matrix equations and how to find the optimized window constants. Four new differentiator windows as a family are obtained. These windows belong to the fixed window. Different from existing windows, the new windows are optimized in terms of reducing the relative errors of the passband. Comparisons show that new windows are better or much better than the Hanning, Hamming, Blackman, Kaiser, Chebyshev and polynomial windows in terms of differentiator performances.     

New design of full band differentiators based on Taylor series

The classical central difference approximations of the derivative of a function based on Taylor series are the same as type III maximally linear digital differentiators for low frequencies. A new finite difference formula is derived which can be implemented as a full band type IV maximally linear differentiator. The differentiator is compared with type III maximally linear and type IV equiripple minimax differentiators. A modification is proposed in the design to minimise the region of inaccuracy near the Nyquist frequency edge     

Integrator and differentiator with time constant multiplicationusing current feedback amplifier

A set comprising an active RC integrator and differentiator with time constant multiplication is presented. The proposed integrator and the differentiator can be used for low-frequency signal processing applications. Moreover, no extremely large-valued passive components are needed. In the integrator, the unlimited multiplication of time constants is allowed. Both have been implemented using commercially available current feedback amplifiers. Experimental results demonstrate the theoretical predictions     

基于差分器的开关电流高通梯形滤波器的设计

本文应用一种新型的双线性/前馈差分器(BFD)来设计开关电流(SI)高通梯形滤波器。这种BFD是用本文提出的SI模块,通用差分器(GD)构成的,此GD具有多种差分功能。文中按S域频带变换和Z域带变换分别介绍了两种不同的设计方法,还给出了Chebyshev高通滤波器和椭圆(Elliptic)高通滤波器设计的实例。     

Novel Approach to Analog-to-Digital Transforms

A novel approach to analog-to-digital transforms, s-to-z transforms, is presented. The approach applies the Boxer-Thaler expansion to a leaky differentiator or to a leaky integrator instead of an ideal differentiator or integrator. The bilinear (Tustin) and the matched pole-zero (MPZ) transformation are special realizations of the new transforms, with an additional built-in prewarping and additional built-in zero placement, respectively. Examples are presented that demonstrate the viability of the approach where the proposed method is compared with the least-squares, bilinear (Tustin), and MPZ transformations