On the design of FIR digital differentiators which are maximallylinear at the frequency π/p, p ∈ {positiveintegers}

Digital differentiators (DDs) which are maximally linear at the spot frequency ω=π/p, p ∈ {positive integers} are proposed for operation over a narrow band of frequencies. The suggested DDs, besides giving zero phase error over the entire band of frequencies (-π⩽ω⩽π), can achieve very high accuracy in the magnitude response, over a given frequency range, with attractively low order of structure. For example, for p=3, magnitude accuracy better than 99.999% can be achieved over the passband 0.26π⩽ω⩽0.41π with an order of structure of 21. Mathematical formulas for the weighting coefficients required in the design have also been given     

Current follower based reconfigurable integrator/differentiator circuits with passive and active components׳ reuse

Reconfigurable integrator/differentiator circuits based on the current follower are presented. They are essential for realizing configurable analog blocks (CABs) for field programmable analog arrays (FPAAs). The proposed circuits provide functional reconfigurations and components reuse. These functions provide flexibility in the area of filter design within CAB architectures. Circuits based on current follower have the potential to operate at higher frequency ranges and offer improved linearity over their counterparts based on the operational amplifier and transconductance amplifier, respectively. No switches are used in a signal path in order to avoid degrading the frequency response of the proposed circuits. A CMOS current follower realization compatible with implementation of the proposed designs is adopted. Experimental results obtained from a standard 0.35 µm CMOS process are provided.     

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 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     

A Low-Pass Prototype Network for Microwave Linear Phase Filters

A new approximation theory is presented for a low-pass prototype filter which simultaneously optimizes both the passband amplitude and phase response of the scattering transfer coefficient over the same finite band. This closed form solution is expressed in terms of single polynomial, which is readily generated through a simple recurrence formula, and has been termed the equidistant linear phase polynomial since its phase deviation from linearity vanishes at equidistant points along the real frequency axis. A synthesis procedure is presented for the realization of this transfer function using a resistively terminated, symmetrical, lossless, two-port network where extensive use is made of the immittance inverter concept. The even-mode admittance, which defines the network, possesses a simple closed form representation in terms of the equidistant linear phase polynomial and its derivative, and consequently, the entire theory is derived in an analytic form. Typical performance characteristics are graphically presented for networks of up to 14th degree, illustrating the superiority of this new approach over any other known form of approximation theory for selective linear phase filters.     

中长波红外探测器非线性度分析

线性度作为评价探测器性能参数的一个重要指标,直接影响着用户的使用状况。以中长波两个波段的探测器作为实验器件,分析讨论了以全波段黑体辐照功率与像元响应率线性拟合及以波段辐照功率与输出信号电压进行线性拟合的两种不同的评价方案。全波段黑体辐照功率拟合出的线性度结果较差,非线性度在6 %左右,而采用波段辐照功率拟合出的非线性度均在0.5 %以内。最终确定以波段辐照功率拟合出的线性度有较高的准确性,为直观评价探测器性能的优劣提供了指导依据。     

A model-based parameter estimation technique for wide-band interpolation of periodic moment method impedance matrices with application to genetic algorithm optimization of frequency selective surfaces

A model-based parameter estimation (MBPE) technique is introduced in this paper for efficiently interpolating periodic moment method (PMM) impedance matrices over a wide frequency band. In the model, only the Floquet harmonics that strongly affect the frequency band of interest are employed to approximate the matrix elements, while the contributions from all other higher-order harmonics are compactly represented by two additional terms. The derivation of the model is physics-based, and the objective is to find the coefficients of the terms in the model by utilizing the values of the impedance matrix elements calculated via PMM at only a few frequency points. The number and position of these fitting points can be pre-determined from the cutoff frequencies of the Floquet harmonics, which allows the MBPE interpolation process in this case to be completely automated. In other words, the number and position of the sampling points are only dictated by the periodicity of the frequency selective surface (FSS) structure and the frequency range of interest. Unlike many of the other scattering parameter-based techniques, the shape and the resonances in the response of the FSS do not have any impact on the construction of the interpolation model. This makes it particularly useful in genetic algorithm (GA) aided FSS design, since for a fixed periodicity and frequency range the MBPE interpolation is independent of the scattering response of candidate FSS designs. Several examples of the new PMM-MBPE approach are presented including one in which it is used to considerably speed up the GA-based design process for a reconfigurable FSS.     

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.     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

Design of adjustable fractional order differentiator using expansion of ideal frequency response

In this paper, the design and implementation structures of adjustable fractional order differentiator (AFOD) are presented. First, the series expansion of ideal frequency response is used to transform the design of AFOD into the designs of log differentiators with various orders. Then, conventional FIR filter design method is applied to design log differentiators. The proposed method is flexible because the AFOD can be designed by considering the trade-off among the storage requirement of filter coefficients, implementation complexity and delay of filter. Finally, several numerical examples are shown to illustrate the effectiveness of the proposed design approach.     

Analog wavelet transform using multiple-loop feedback switched-current filters and simulated annealing algorithms

A new approach for implementing continuous wavelet transform (CWT) based on multiple-loop feedback (MLF) switched-current (SI) filters and simulated annealing algorithms (SAA) is presented. First, the approximation function of wavelet bases is performed by employing SAA. This approach allows for the circuit implementation of any other wavelets. Then the wavelet filter whose impulse response is the wavelet approximation function is designed using MLF architectures, which is constructed with SI differentiators and multi-output cascade current source circuits. Finally, the CWT is implemented by controlling the clock frequency of wavelet filter banks. Simulation results of the proposed circuits and the filter banks show the advantages of such new designs.     

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.     

Recurrence model analysis for multiple waveguide discontinuitiesand its application to circular structures

A general formulation for the scattering from multiple waveguide discontinuities is presented. It is based on the modal analysis technique in which the corresponding fields are expanded in terms of vector eigenfunctions and the boundary conditions are imposed at each junction. Analytic expressions for the global scattering matrices are derived using a recurrence procedure that requires substantially less computation than the traditional cascading techniques. The matrix equations are truncated in a manner that satisfies the conditions for a good overall convergence, which is illustrated for step discontinuities in circular waveguides. Numerical results are presented for a thick iris in a circular waveguide and for iris-matched dielectric window designs     

High-linearity continuous-time filter in 5-V VLSI CMOS

High-linearity self-tuning continuous-time filters, fabricated in a standard 1.6-μm 5-V CMOS process, are presented. Frequency control is achieved using switchable arrays of highly linear double-polysilicon capacitors in an active RC filter structure, resulting in tunable filters with very low signal distortion. One filter, a Tow-Thomas biquad, exhibits dynamic range and signal linearity of typically 91 dB. Another smaller implementation, a Sallen and Key filter, attains ⩾76 dB. Cutoff frequency response is maintained to an accuracy of around ±5%     

The photorefractive effect—a review

Photorefractive materials have been assuming ever increasing prominence in the non-linear optics field due to their unique capability for displaying strong non-linear effects at milliwatt power levels. In this review we describe in some detail the two currently accepted models of the photorefractive process. The “band transport” model assumes that photo excited electrons (or holes) are ejected from filled donor (or acceptor) sites to the conduction (or valence) band where they migrate to dark regions in the crystal before recombining into empty traps. The charge separation results in a space charge field which modulates the refractive index via the linear electro-optic effect. The “hopping” model assumes that carrier transport occurs via light induced hopping from a filled donor site to a neighbouring empty trap. In particular, we examine the timeand spatial frequency dependence of grating formation and discuss the validity of the simplified model of a material response linear in modulation ratio (fringe contrast). In addition we show that the “hopping” model although physically distinct from the band transport model is described by equations which can be considered as a special case of the band transport equations. Results of a complete numerical simulation of the band transport model are presented to illustrate the properties of the photorefractive effect and to test the validity of the simplified model.The two models are normally formulated for an isotropic material illuminated by two plane wave beams which are assumed to be unaffected by the material. Photorefractive materials, however, are naturally anisotropic and in applications one is often interested in non-plane wave beams. We present for the first time an extension of the model to non-plane wave beams and explicity take full account of the vectorial nature of light and the crystal anisotropy. Barium titanate is used as an example to illustrate the extended model and graphs are presented which show the dependence of the nonlinearity on beam angles, polarisation and crystal orientation.Finally we discuss some applications is non-linear optics which exploit some of the unique features of the photorefractive effect. The photorefractive effect is illustrated throughout the paper by experimental results performed in our own laboratory.     

Improved design of digital fractional-order differentiators using fractional sample delay

In this paper, a digital fractional-order differentiator (FOD) is designed by using fractional sample delay. To improve the design accuracy of conventional fractional differencing and Tustin design methods at high frequency regions, the integer delay is replaced by fractional sample delay. By using the well-documented finite-impulse-response Lagrange, infinite impulse response allpass, and Farrow fractional delay filters, the proposed FOD can be implemented easily even though the fractional sample delay is introduced. Several design examples are illustrated to demonstrate the effectiveness of the proposed method.     

Novel micromachined lumped band pass filter for 5.2 GHz WLAN applications

This paper describes the design, manufacturing and experiments of a lumped element band pass filter in a new topology. The design starts from a second order capacitive coupled resonator topology. An additional series inductor is inserted in the filter classical topology, for shifting two transmission zeros on the real frequency axes in the filter's band stop, to improve the high frequency response. Design equations for the new band stop resonance frequency are presented together with the analysis of the correspondence between the band pass and band stop attenuation vs. the quality factor of the shunt and series inductors used. The filter is supported on a 6.4 μm thin dielectric membrane, and is manufactured using silicon micromachining, in CPW technology. Measurements illustrated a minimum 2.75 dB insertion loss at 5.5 GHz in the band pass, and more than 40 dB attenuation, at 8 GHz.     

Cheby?shev time-domain deconvolution for transversal filter equalisers

Design equations are presented for computing the N tap weights of a transversal filter equaliser. The associated time-domain deconvolution is performed subject to the Cheby?shev (minimax) error criterion. Individual or pointwise deconvolution errors are controlled and minimised uniformly. This method offers an alternative to least square error or discrete Fourier transform designs wherein only the cumulative de-convolution error is minimised. Computationally, the Ascent algorithm is used which requires inversion of two (N + 1) × (N + 1) matrices followed by a finite number of elementary algebraic exchange operations. The equations needed to implement this algorithm are presented in a form suitable for digital computation.     

Generation of two-dimensional spatial and temporal propertiesthrough spatiotemporal convergence between one-dimensional neurons

Primary otolith afferents are characterized by diverse temporal and spatial response properties. The temporal properties of these neurons vary from tonic to phasic response characteristics during stimulation with linear acceleration. This study examines the response properties of target neurons that arise from spatiotemporal convergence (STC) between purely tonic and phasic-tonic afferents. The transfer function of the phasic-tonic afferent is described by either fractional leaky differentiator or integrator terms. Target neurons would generally exhibit two-dimensional spatial sensitivity and are characterized by two perpendicular response vectors. It is shown that target neurons have different temporal properties during stimulation along different spatial directions. Specifically, they could exhibit tonic temporal response dynamics during stimulation along the second response vector. The phasic dynamics along one response vector are described by a complete ideal differentiator for frequencies below the corner frequency of the leaky operator terms     

Calculation of the frequency characteristics of the electromagnetic radiation of waveguide-horn antennas

A method for calculation of the frequency characteristics of the electromagnetic radiation of waveguide-horn antennas is proposed. The method is based of frequency expansions of the field of the electromagnetic radiation of the antenna excited by auxiliary finite pulses. This radiation is calculated with the use of the method of nonstationary waveguide equations and the concept of a virtual electromagnetic waveguide. Examples of calculation of the amplitude-phase characteristics of the circuit and radiation patterns at fixed frequencies are presented. It is shown that a high accuracy of determination of frequency characteristics is attainable in rather wide frequency band.