全通多相网络滤波器组的理论和设计

本文进一步研究了应用全通滤波器实现均匀N带滤波器组的设计理论。我们提出了一种两级全通型滤波器组的结构,第一级为周期性镜像半带滤波器,第二级为两个N/2带的带通滤波器组。第一级的阻带恰好可以抑制第二级的不可控带,实现了全通型多相滤波器的连续阻带持性。并且给出了综合滤波器组的实现方案,可以使整个分析/综合系统完全消除混叠和幅度失真。最后本文给出了一个实例。     

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison     

一种数字全通滤波器的设计方法研究

研究了一种数字全通滤波器的设计方法.对于一个平稳的全通滤波器,其分母多项式一定具有最小相位.该方法是基于最小相位滤波器的复倒谱系数和其群迟延函数以及其系统函数之间的关系,通过一个非线性的递归方程求解分母多项式的系数.由全通滤波器的特性已知,分母系数可以完全决定全通滤波器的传递函数.仿真结果表明这种方法能够使所设计滤波器的群延迟特性在整个频率范围内以近似理想的群延迟特性存在.并结合实现提出了一种用FIR逼近IIR的方法.     

The design of arbitrary FIR digital filters using the eigenfiltermethod

The design of finite impulse response (FIR) digital filters for approximating an arbitrary function (in both magnitude and phase) in the least-square sense is studied. The design method is based on the computation of an eigenvector of an appropriate real, symmetric and positive-definite matrix. The design of the complex-coefficient filter is shown to be an extension of the design of the real-coefficient filter. Several design examples, including the constant-group-delay filters and digital phase all-pass filters, are presented. Comparisons to existing methods are made     

A new approach to the design of complex all-pass IIR digital filters

A new method is proposed for designing complex all-pass IIR filters, the all-pass IIR filters with complex coefficients, in this paper. By minimizing the integration of certain square phase error over interested frequencies, an eigenvector of an appropriate real, symmetric and positive-definite matrix is computed to get the filter coefficients. The stability is achieved by specifying properly the desired phase specifications. If an appropriate iterative process is used, equiripple complex all-pass filter design can be obtained. The method is simple and the performance is comparable to the existing methods. Several examples are presented to demonstrate the effectiveness of the approach.     

Closed-form approach to design of all-pass digital filters using cepstral coefficients

A simple method for the design of all-pass digital filters is described. In this method, given a desired group delay, the cepstral coefficients corresponding to the denominator of a stable all-pass filter are determined using a least-squares approach. The coefficients of the all-pass filter are then obtained from the cepstral coefficients using a recursive relation.     

基于巴特沃斯逼近的二维IIR数字滤波器的设计

本文给出了一种基于巴特沃斯逼近的二维ＩＩＲ数字滤波器的设计方法，得到了由基本的全通节级联，并联实现的各种二维滤波器函数，包括，镜象对称互补滤波器，扇形滤波器和具有任意矩形通、阻带的滤波器，结果表明，这种实现结构具有通有灵敏度低、滤波器系数少的优点，并且由于巴特沃斯逼近的最大平坦性，得到的滤波器具有良好的相位特性。     

Analytical Synthesis of Low-Sensitivity High-Order Voltage-Mode DDCC and FDCCII-Grounded R and C All-Pass Filter Structures

The difficulty of realizing the operations of addition and subtraction of a voltage-mode signal renders two special active elements, namely, differential difference current conveyors (DDCCs) and fully differential current conveyors (FDCCIIs), both of which have the ability to perform the operations of addition and subtraction, to become very important for voltage-mode analog filter design. Note that, for the design of operational transconductance amplifier and capacitor (OTA-C) filters, the recently reported analytical synthesis methods (ASMs) have been shown to be very effective for achieving simultaneously the three criteria, namely, all capacitors being grounded, the use of the minimum number of active and passive components, and the use of single-ended input OTAs. However, none of the ASMs uses DDCCs and FDCCIIs in the design of voltage-mode filters. In this paper, a method of realizing DDCC and FDCCII-based all-pass filter structures with either equal capacitances or equal conductances through a new ASM is presented. Only n current conveyors (the least number of active components), n grounded capacitors, and grounded resistors (the minimum number of passive components) are used for realizing an nth-order voltage-mode all-pass filter structure. Moreover, the new all-pass filter structure synthesized by the new ASM achieves very low individual as well as near-null group sensitivities just as in the case of the passive LC ladder filters, has very low power consumption, a low component spread for equal denominator conductance design, and a high input impedance which is attractive from the point of view of cascadability. Finally, H-Spice simulations, using 0.35-mum process and plusmn1.65-V supply voltages, are included and validate theoretical predictions.     

Design of computationally efficient elliptic IIR filters with areduced number of shift-and-add operations in multipliers

In this paper, a new design method for elliptic IIR filters that provides the implementation of half of the multiplication constants with few shifters and adders is proposed. An IIR filter, when derived by the bilinear transformation from an elliptic minimal Q-factor analog prototype, has its z-plane poles on the circle that is orthogonal to the unit circle and has the center on the real axis of the plane. Due to this property, the center of the circle can be used as a parameter for the representation of a pole, whereas the second parameter is the radius of the pole. It is shown in this paper that the center of the circle is uniquely determined by the frequency for which the filter attenuation is 3 dB. This result is used for the realization based on the parallel connection of two all-pass networks. It is shown that all second-order all-pass sections can be implemented with one common multiplication constant determined by the center of the circle. The design method is presented that, by an appropriate distribution of a margin in the filter performance, predetermines the value of the common constant according to the desired number of shift-and-add operations. This way, half of the multipliers are replaced with a limited number of shifters and adders. Conventional computer programs for IIR elliptic digital filters can be used. The direct approach for the distribution of the z-plane poles among two all-pass functions is developed. The application and efficiency of the proposed design method are demonstrated by examples     

General optical all-pass filter structures for dispersion controlin WDM systems

All-pass filters (APFs) are devices that allow phase correction or equalization without introducing any amplitude distortion. An optical implementation of such devices is very attractive since they can be used for dispersion compensation. In contrast to other dispersion control devices, optical APFs can correct any order of dispersion. This can be achieved by careful design of multistage APFs to approximate a target phase profile. However, large dispersion is usually narrow band or requires many filter stages. These performance tradeoffs and the general phase properties of optical APFs are reviewed and clarified in the first part of this paper. In the second part, a general design methodology of optical APFs is introduced. We show that any all-pass structure may be constructed from simple N-port devices (such as directional couplers or Mach-Zehnder interferometers) with N-1 outputs fed back to any of the N-1 inputs. The feedback paths may contain delays or further APFs (recursive design). This set of design rules allows for constructing complex all-pass filters of any number of stages starting with very simple elements. We use this technique to demonstrate a number of optical all-pass structures that may be implemented in planar waveguide or using thin-film filter technology     

基于全通函数的线性相位参量均衡器的设计

本文提出一种线性相位参量均衡器的设计方法,该方法通过构造具有理想相位响应的全通函数和频域变换实现参量均衡器的设计。此外,通过级联全通函数使参量均衡器具有线性相位属性,从而提高了它的应用价值。     

A Very Efficient Approach for the Synthesis of 2-D Recursive Fan Filters

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Design of IIR Notch Filter with Approximately Linear Phase

A method for design of linear phase notch IIR filters is presented in this paper. The filter is realized in the form of a?parallel connection of two all-pass sub-filters. In order to achieve the resulting filter with an approximately linear phase in the pass-band, the applied all-pass sub-filters should be also with a?linear phase. The desired amplitude characteristic of a?resulting filter is obtained by all-pass sub-filter phase approximation. It can be achieved by applying either a?pure delay or an IIR all-pass filter in one branch. If a?pure delay is positioned in one branch, equiripple phase of all-pass sub-filter from the other branch is guaranteed for an equiripple amplitude characteristic of the resulting filter. Efficiency of the proposed algorithm is demonstrated on a?few examples. The algorithm exhibits a?fast convergence and an easy determination of initial values. In the case where IIR all-pass sub-filters are placed in both branches, the resulting amplitude characteristic satisfies all the prescribed demands, but the amplitude characteristic is not equiripple even when both all-pass sub-filters have equiripple phase.     

Supplementary all-pass sections with reduced number of passive elements using a single current conveyor

Four new configurations realizing current conveyor-based first-order all-pass filters are proposed. Using these configurations two types of first-order voltage-mode allpass filter can be realized. The circuits employ a single positive type secondgeneration current conveyor (CCII+) and only three passive components. For each topology only a simple component matching constraint is required. To illustrate the design possibilities provided by the introduced circuits an oscillator circuit consisting of the proposed all-pass filters is constructed and experimentally tested.     

An efficient approach for the synthesis of 2-D recursive fanfilters using 1-D prototypes

An elliptic approximation-based design approach is proposed for obtaining 2-D recursive fan filters. The 1-D elliptic filter is reduced to a cascade-parallel combination of all-pass sections and is then used as a prototype for fan filter synthesis, resulting in final realization of 2-D transfer functions using allpass filters. It is shown that the synthesis procedure not only gives a filter that has far fewer coefficients but also enjoys a very low computational complexity     

Generalized WLS Method for Designing All-Pass Variable Fractional-Delay Digital Filters

This paper presents an optimal weighted least squares (WLS) method for designing low-complexity all-pass variable fractional-delay (VFD) digital filters. Instead of using a fixed range for the VFD parameter p and same-order constant-coefficient filters (subfilters), both the VFD parameter range p isin [p _Min,p _Max] and subfilter orders are optimized such that a low-complexity all-pass VFD filter can be achieved for the LS design. To suppress the peak errors of variable frequency response, weighting functions are adopted and optimized such that the boundary peak errors can be further reduced but without noticeably increasing the total error energy (integral of squared error) of variable frequency response. After optimizing the variable range of the VFD parameter, weighting functions, and subfilter orders, an all-pass VFD filter can be designed by using a generalized noniterative WLS method, which yields a closed-form solution. Design examples are given to illustrate that utilizing different-order subfilters, along with the optimal range and optimal weighting functions, can yield an all-pass VFD filter with significantly reduced complexity and design errors as compared with existing ones.     

The design of digital all-pass filters using second-order cone programming (SOCP)

This brief proposes a new method for designing digital all-pass filters with a minimax design criterion using second-order cone programming (SOCP). Unlike other all-pass filter design methods, additional linear constraints can be readily incorporated. The overall design problem can be solved through a series of linear programming subproblems and the bisection search algorithm. The convergence of the algorithm is guaranteed. Nonlinear constraints such as the pole radius constraint of the filters can be formulated as additional SOCP constraints using Rouche's theorem. It was found that the pole radius constraint allows an additional tradeoff between the approximation error and the stability margin. The effectiveness of the proposed method is demonstrated by several design examples and comparison with conventional methods.     

Trade-offs in the OTA-based analog filter design

Operational transconductance amplifiers (OTAs) are widely used in the design of electronically tunable circuits. However, electronic tunability ranges of the OTA based filters are restricted by the limited bandwidth of the transconductance gain of the OTA. Furthermore, stability conditions and the linearity of the OTA which depends on the control current restrict the tunability. In this paper, some trade-offs in the electronically tunable filters are investigated. In addition, the tunability ranges of some first and second order OTA-C and OTA-RC filters are comparatively examined. Moreover, an OTA-C all-pass filter circuit is presented. SPICE simulations are performed and stability analyses are given for both of the OTA-C and OTA-RC filters. Operation of the presented all-pass filter is verified experimentally.     

A step-by-step active-filter design

This article presents, in a simplified manner, a design method for active filters intended for those who are not filter specialists. By following the described five-step approach, a circuit designer who has some knowledge of passive filters will (without having to learn a whole new technology) be able to design active filters just as easily as he now handles conventional passive filters. Starting with the filter specification, it is shown sequentially how to realize a network that meets the prescribed requirements. Configurations and element values are given for the low-pass (LP), bandpass (BP), high-pass (HP), all-pass (AP), and band-elimination (BE), second-order active filter building blocks.     

Eigenfilter approach for the design of variable fractional delay FIR and all-pass filters

An eigenfilter approach is presented for designing 1-D and 2-D variable fractional delay FIR and all-pass filters. First, the coefficients of filters are expressed as a polynomial of the fractional delay parameter. Then, the optimal polynomial coefficients are obtained from the elements of the eigenvector corresponding to the minimum eigenvalue of a real, symmetric and positive definite matrix. Finally, several design examples of 1-D and 2-D variable fractional delay FIR and all-pass filters are used to illustrate the effectiveness of the eigenfilter approach.