A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response (FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomials and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variable bandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the above polynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order to determine the filter coefficients, mean squared difference between the desired variable bandwidth filter and the practical filter is minimized by differentiating it with respect to its coefficients leading to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. Several examples are included to demonstrate effectiveness of the proposed method in terms of passband error (e_p), stopband error (e_s) and stopband attenuation (A_s).     

Non-fragile <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript> and <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filter designs for polytopic two-dimensional systems in Roesser model

This paper is concerned with the problem of non-fragile H ₂ and H _∞ filter designs for two-dimensional (2-D) discrete systems in Roesser model with polytopic uncertainties. The filters to be designed are assumed to be with additive norm-bounded coefficient variations which reflect the imprecision in filter implementation. The complicated filter design problem is successfully tackled by using the slack variable technique and imposing a structural restriction on the slack matrix. Explicit expressions of the non-fragile H ₂ and H _∞ filters are given in terms of solutions to a set of linear matrix inequalities (LMIs). An illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.     

A Delay Partitioning Approach to H �� Filtering for?Continuous Time-Delay Systems

This paper investigates the problem of delay-dependent H _∞ filter design for continuous time-delay systems. Attention is focused on the design of linear filters guaranteeing a prescribed noise attenuation level in an H _∞ sense. The admissible filters can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities (LMIs), which can be readily solved via standard software. The crucial issue for solving the filter design problem is the utilization of the delay partitioning idea, which proves to be less conservative than most of the existing results, and the conservatism could be notably reduced by thinning the delay partitioning. Numerical examples are provided to show the effectiveness and the advantage of the proposed filter design method.     

Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries

In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section.     

电磁寄生参数在高频SAW滤波器设计中的应用

在设计高频声表面波(SAW)滤波器的过程中,若只考虑封装壳和键合线的电磁寄生参数而忽略汇流条的电磁寄生参数,则SAW滤波器的实际性能易受汇流条寄生参数影响而出现通带波动和驻波增大等问题。该文拟用电声-电磁联合仿真方法设计高频SAW滤波器以解决汇流条寄生参数对SAW滤波器性能的影响。通过此方法研制的滤波器通带插入损耗小于1 dB,波动0.5 dB,通带内驻波最大值2.1,-1.5 dB带宽75.7 MHz,-3 dB带宽84 MHz (相对带宽为4.8%),-30 dB带宽112 MHz,BW_{-3 dB}/BW_{-30 dB}矩形系数1.33。包含封装壳、键合线及汇流条的寄生参数的理论仿真结果与实验测试结果吻合较好,表明了采用此模型设计高频SAW滤波器的可行性。     

FIR design by non-uniform sampling in frequency domain

In this paper an expression for H(z) has been derived in terms of N independent samples {H_k }. It has then been used to examine effects of non-uniform frequency sampling on the resultant frequency response of FIR filters. This has been applied first to the non-uniform sampling in both the passband and stopband, of a desired filter, and then to non-uniform sampling in the stopband only. Several lowpass filter designs have been examined by these methods and results discussed.     

Symmetric self-Hilbertian filters via extended zero-pinning

A symmetric self-Hilbertian filter is a product filter that can be used to construct orthonormal Hilbert-pair of wavelets for the dual-tree complex wavelet transform. Previously reported techniques for its design does not allow control of the filter's frequency response sharpness. The Zero-Pinning (ZP) technique is a simple and versatile way to design orthonormal wavelet filters. ZP allows the shaping of the frequency response of the wavelet filter by strategically pinning some of the zeros of the parametric Bernstein polynomial. The non-zero Bernstein parameters, α_i's, are the free-parameters and are constrained in number to be twice the number of pinned zeros in ZP. An extension to ZP is presented here where the number of free-parameters is greater than twice the number of pinned zeros. This paper will show how the extended ZP can be used to the design of Hilbert pairs with the ability to shape the filter response.     

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

The problem of nonfragile robust H _∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H _∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.     

A microstrip folded compact wideband band-pass filter with wide upper stopband

A miniaturized wideband band-pass filter with a 3-dB fractional bandwidth of 109.3% (1.53 GHz to 5.22 GHz), high out-of-band attenuation greater than 25 dB, and wide upper stopband up to 14 GHz is proposed. The design consists of a dual-composite right/left handed resonator, embedded open-circuited stub, and a pair of quarter-wavelength short-circuited stubs. These elements are coupled in the near distance to form a miniature filter with a compact occupied area of 0.21 λ _g × 0.19 λ _g (≈ 0.013 cm²). The optimized filter has multi-transmission poles in the passband, substantially improving the return loss and insertion loss characteristics. The behavior of the passband and stopband is verified against the results of a lumped element model and matrix analysis with a full-wave moment-based analysis and actual measurements. The results of this verification and a comparison with the performance of filters in other references indicate that the proposed filter is very efficient and applicable to compact microwave systems.     

Two-stage, least squares design of biorthogonal filter banks

A two-stage approach is employed for the design of a class of two-channel biorthogonal filter banks. The filter banks belong to the class HPFB (halfband pair filter bank) and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The design of the free parameters of the Bernstein polynomial is achieved through a least squares method. In the first stage, the analysis low-pass filter is designed and in the second stage, the synthesis lowpass filter is designed. With the two-stage approach, the design process is efficient and involves solving linear equations. The design technique allows filters with different characteristics to be designed easily.     

A microstrip wideband bandpass filter based on λ/2 stub with spurious passband suppression scheme

In the design of bandpass filters, the use of λ/2 stubs of shunt configuration had been mostly unacceptable due to their effect of narrow stopband bandwidths in the ensuing filters. The design of bandpass filter presented in this article introduces 360° series transmission line segments to increase the stopband bandwidths to an acceptable level without affecting the wide passband. This designed filter has low insertion loss of less than –1.98 dB and a fractional bandwidth of 50% at 6 GHz mid-band frequency. A sharp rejection in the stopband is observed. To further widen the bandwidth of stopbands, a series capacitor and a shunt stub are used. The transmission line model of the filter is in good agreement with measured results. The filter is planar and is fabricated on FR-4 substrate which makes it cost-effective and easy to fabricate.     

General Coupling Matrix Synthesis Method for Microwave Resonator Filters of Arbitrary Topology

This letter presents a new approach to synthesize the resonator filters of an arbitrary topology. This method employs an optimization method based on the relation between the polynomial coefficients of the transfer function and those of the S₂₁ from the coupling matrix. Therefore, this new method can also be applied to self‐equalized filters that were not considered in the conventional optimization methods. Two microwave filters, a symmetric 4‐pole filter with four transmission zeros (TZs) and an asymmetric 8‐pole filter with seven TZs, are synthesized using the present method for validation. Excellent agreement between the response of the transfer function and that of the synthesized S₂₁ from the coupling matrix is shown.     

Ultra wideband filter using dumbbell-etched stepped impedance resonator

In this article, an ultra wideband bandpass filter using the dumbbell-etched stepped impedance resonator (SIR) is presented. The filter consists of a dumbbell-etched SIR with an impedance ratio K?>?1 and the enhanced coupled input/output lines. The SIR is folded into a dumbbell shape to achieve a smaller circuit size than the filter with conventional SIR. The bandwidth can be analysed using the image-parameter method to obtain the proper dimension of the coupled lines and verified using electromagnetic simulation. The measured 3?dB fractional bandwidth of 110% and insertion loss |S ₂₁| less than 3?dB over the entire passband are achieved.     

Biorthogonal nearly coiflet wavelets for image compression

Filter bank design for wavelet compression is crucial; careful design enables superior quality for broad classes of images. The Bernstein basis for frequency-domain construction of biorthogonal nearly coiflet (BNC) wavelet bases forms a unified design framework for high-performance medium-length filters. A common filter bandwidth is characteristic of widely favoured BNC filter pairs: the classical CDF 9/7, the Villasenor 6/10, and the Villasenor 10/18. Based on this observation, we construct previously unknown BNC 17/11 and BNC 16/8 wavelet filters. Key filter-quality evaluation metrics, due to Villasenor, demonstrate these filters to be well suited for image compression. Also studied are the biorthogonal coiflet 17/11 (half-band), 18/10 and 10/6 filter pairs, which have not previously been formally evaluated for image coding. Simulation results confirm that the BNC 17/11 and BNC 16/8 wavelet bases are outstanding for compression of natural and medical images, and particularly for images with significant high-frequency detail, such as fingerprints. The BNC 17/11 pair recommends itself for international standardization for the compression of still images; the BNC 16/8 pair for high-quality compression of production quality video. Experimental evidence suggests biorthogonal filters achieve good compression if, subject to a filter bandwidth constraint, maximum vanishing moments are obtained for a given filter support.     

Tuning of FIR filter transition bandwidth using fractional Fourier transform

The transition bandwidth of window-based FIR filters is proportional to the window main-lobe width, which in turn is proportional to the length of the window function. As such, transition bandwidth of FIR filters can be directly tuned by varying window length for on-line tuning applications. However, analysis of window functions in fractional Fourier domain, a generalization of Fourier domain, also establishes the dependence of window main-lobe width on the order of fractional Fourier transform (FRFT). Thus, an alternative methodology to tune the transition bandwidth, based on FRFT, is developed in this work. The proposed methodology is useful for frequency domain filtering and introduces a comparative ease in tuning by eliminating the need to re-compute the impulse response coefficients. Also, significant computational saving has been achieved using FRFT. However, it is observed that the direct approach can introduce a lot more adjustability in the transition bandwidth than the FRFT approach. Apart from Kaiser window, considered to be optimum for FIR filter design, another window with a high side-lobe fall-off-rate (SLFOR), viz, Parzen-cos⁶ (πt) (PC6), has also been used in the proposed on-line filter tuning. Better performance of windows with high SLFOR in on-line sharpening is illustrated with the aid of simulation results.     

基于LiTaO3基片宽带声表面波滤波器设计方法

通讯系统传输效率的提升对滤波器带宽的要求越来越高,如果使用常规声表面波(SAW)滤波器设计技术,则将面临损耗大或带宽达不到要求的问题。该文根据系列宽带SAW滤波器产品开发结果,总结了采用特殊技术用LiTaO₃压电基片实现相对带宽8%以上的宽带SAW滤波器设计方法,其包括利用外围电感、电容增加SAW谐振器的谐振频率和反谐振频率的间隔,提高阻抗元滤波器带宽;利用多模式纵向耦合谐振滤波器结构增加滤波器带宽;利用双通带滤波器并联结构获得大带宽滤波器。上述方法各有优缺点,其均能获得约为9%的带宽。     

Narrow-band vertically stacked filters in InGaAlAs/InP at 1.5 μm

A narrow-band wavelength filter in InGaAlAs/InP has been modeled, fabricated, and tested. A highly asymmetrical, vertically coupled directional coupler operating near the band-edge is formed by a narrow ridge and a wide strip-loaded waveguide. The results of numerical simulation, performed by employing the spectral index method, effective-index method, and a modified coupled-mode theory, are used to fabricate a filter structure with a prescribed filter response. Operation at a center wavelength around 1.5 μm with a bandwidth of 18 Å and transfer efficiency of ~46-68% is achieved. Excellent agreement between the. Designed and measured bandwidth is demonstrated. A multichannel filter device based on an array of individual filters that is capable of extending the usable spectral range is analyzed     

Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay

This paper presents central finite-dimensional H _∞ filters for linear systems with state or measurement delay that are suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including an attenuation control term with opposite sign. In contrast to the results previously obtained for linear time-delay systems, the paper reduces the original H _∞ filtering problems to H ₂ (optimal mean-square) filtering problems, using the technique proposed in Doyle et al. (IEEE Trans. Automat. Contr. AC-34:831–847, 1989). The paper first presents a central suboptimal H _∞ filter for linear systems with state delay, based on the optimal H ₂ filter from Basin et al. (IEEE Trans. Automat. Contr. AC-50:684–690, 2005), which contains a finite number of filtering equations for any fixed filtering horizon, but this number grows unboundedly as time goes to infinity. To overcome that difficulty, an alternative central suboptimal H _∞ filter is designed for linear systems with state delay, which is based on the alternative optimal H ₂ filter from Basin et al. (Int. J. Adapt. Control Signal Process. 20(10):509–517, 2006). Then, the paper presents a central suboptimal H _∞ filter for linear systems with measurement delay, based on the optimal H ₂ filter from Basin and Martinez-Zuniga (Int. J. Robust Nonlinear Control 14(8):685–696, 2004). Numerical simulations are conducted to verify the performance of the designed three central suboptimal filters for linear systems with state or measurement delay against the central suboptimal H _∞ filter available for linear systems without delays. The authors thank The London Royal Society (RS) and the Mexican National Science and Technology Council (CONACyT) for financial support under an RS International Incoming Short Visits 2006/R4 Grant and CONACyT Grants 55584 and 52953.     

An LMI-Based Method for Reference Spur Reduction in Charge-Pump Phase-Locked Loops Containing Loop Delay

This paper presents a loop-filter design method for third-order charge-pump phase-locked loops containing the loop delay. This method is derived from a z-domain phase-locked loop model. For a given loop bandwidth, we employ ripple swing control and adjust the filter pole to improve the spur performance. Another dynamic specification, the jitter peaking, is formulated as a H _∞ performance. The loop-filter design is transformed into an H _∞ optimization problem with the ripple swing constraint, which is solved using convex programming skills (linear matrix inequality, LMI). Compared to the conventional method, the method proposed in this study offers greater spur reduction without altering the loop bandwidth.     

Dispersive properties of optical filters for WDM systems

Wavelength division multiplexing (WDM) communication systems invariably require good optical filters meeting stringent requirements on their amplitude response, the ideal being a perfectly rectangular filter. To achieve high bandwidth utilization, the phase response of these filters is of equal importance, with the ideal filter having perfectly linear phase and therefore constant time delay and no dispersion. This aspect of optical filters for WDM systems has not received much attention until very recently. It is the objective of this paper to consider the phase response and resulting dispersion of optical filters in general and their impact on WDM system performance. To this end we use general concepts from linear systems, in particular, minimum and nonminimum phase response and the applicability of Hilbert transforms (also known as Kramers-Kronig relations). We analyze three different classes of optical filters, which are currently being used in WDM systems and compare their performance in terms of their phase response. Finally, we consider possible ways of linearizing the phase response without affecting the amplitude response, in an attempt to approximate the ideal filter and achieve the highest bandwidth utilization