过采样精确重构余弦调制滤波器组的设计

本文首先推导出过采样滤波器组精确重构的条件,由于此时所需的约束条件数比临界采样时少,因而可以设计出频域衰减特性更好的滤波器用,然后提出了精确重构约束条件下原型概通江波器的一种新的设计方法,采用矢的二次型约束优化算法,该算法优化方便,收剑速度快,与其它方法相比,滤波器的阻带衰减大。     

Oversampled cosine-modulated filter banks with arbitrary systemdelay

Design methods for perfect reconstruction (PR) oversampled cosine-modulated filter banks with integer oversampling factors and arbitrary delay are presented. The system delay, which is an important parameter in real-time applications, can be chosen independently of the prototype lengths. Oversampling gives us additional freedom in the filter design process, which can be exploited to find FIR PR prototypes for oversampled filter banks with much higher stopband attenuations than for critically subsampled filter banks. It is shown that for a given analysis prototype, the PR synthesis prototype is not unique. The complete set of solutions is discussed in terms of the nullspace of a matrix operator. For example, oversampling allows the design of PR filter banks having unidentical prototypes (of equal and unequal lengths) for the analysis and synthesis stage. Examples demonstrate the increased design freedom due to oversampling. Finally, it is shown that PR prototypes being designed for the oversampled case can also serve as almost-PR prototypes for critically subsampled cosine-modulated pseudo QMF banks     

Design of perfect-reconstruction nonuniform recombination filter banks with flexible rational sampling factors

This paper studies the design of a class of perfect-reconstruction (PR) nonuniform filter banks (FBs) called recombination nonuniform FBs (RNFBs). They are constructed by merging subbands in a uniform FB with sets of transmultiplexers (TMUXs). It generalizes the RNFBs previously proposed by the authors to allow more general choice of the sampling factors. The spectral inversion and spurious response suppression problems of these new RNFBs using cosine modulation are analyzed, and a simple design method based on a matching condition is proposed. It is also found that the FB and the TMUX in the recombination structure can be designed separately to satisfy the matching condition. In addition, real-time adaptive merging of the channels to provide dynamic nonuniform frequency partitioning is feasible. Another advantage of the RNFBs is that the recombination and processing of the subband signal can be done at the decimated domain of the uniform FB, which greatly reduces its implementation complexity. Design examples show that high quality nonuniform PR FBs with low implementation complexity and variable time-frequency resolution can be obtained by the proposed method.     

Cognitive wideband spectrum sensing using cosine-modulated filter banks

A multichannel joint spectrum sensing strategy based on cosine-modulated filter banks (CMFBs) was developed to improve sensing efficiency. The received wideband signal was split into several bands through the filters that are constructed by grouping continuous sub-band filters. Through flexibly designing prototype filter, not only the spectrum of non-uniform bandwidth can be estimated, but also the spectral leakage between adjacent channels can be adjusted. The probabilities of false alarm and detection for multichannel jointly spectrum sensing in the Rayleigh fading channel were deduced. The decision thresholds of different channels were obtained as regards the probability of false alarm. Simulation results show that compared with the traditional energy detector, the detection capability and sensing efficiency have been improved, especially at low signal-to-noise ratio. The CMFB-based multichannel joint sensing scheme not only increases the efficiency of detection, but also enhances the flexibility on the control of bandwidth and spectral leakage between neighbouring channels.     

一种二阶锥规划通带线性相位FIR滤波器的设计

在有限冲激响应（Finite Impulse Response,FIR）滤波器设计中,如果系统只要求通带或某个频域区间具有线性相位而其他频域区间相位非线性,则系数对称的FIR滤波器设计方法不再适用。为此,提出了一种基于二阶锥规划（Second-Order Cone Programming,SOCP）的通带线性相位FIR滤波器设计方法。该方法使用二阶锥规划实现滤波器设计,其中优化目标为通带最小群延迟,约束条件为全频域振幅误差。实验结果显示,所提方法设计的FIR滤波器有着很好的幅频特性和通带线性相位,通带群延迟误差很小。该方法实现简单,计算复杂度低,可以广泛应用于数字信号处理领域。     

A new approach to the design of critically sampled M-channeluniform-band perfect-reconstruction linear-phase FIR filter banks

A new approach is presented for the design of uniform-band M-channel perfect-reconstruction (PR) FIR filter banks employing linear-phase analysis and synthesis filters. The technique designs on the impulse responses of the analysis filters directly. The design problem is formulated as an optimization program. The filter bank's PR feature can either be implicitly enforced through a set of mathematical relationships among the analysis filters' coefficients or through a set of constraints in the optimization program. The former approach results in a filter bank whose PR feature's dependency on hardware and software is eliminated or, at least, minimized. The synthesis filters are then obtained by a set of relationships that describe each synthesis filter as a function of the analysis filters. The criterion for optimality is “least-squares,” where the square of the difference between the ideal and actual frequency responses is integrated over the appropriate frequency bands for all M analysis filters and minimized     

Numerically efficient optimal design of cosine-modulated filter banks with peak-constrained least-squares behavior

Several current applications related to signal compression and representation and high-speed transmission require very selective filter banks/transmultiplexers. A possible solution is to employ the cosine-modulated filter banks/transmultiplexers (CMFBTs) where the prototype filters satisfy demanding constraints with respect to both the total stopband energy and maximum stopband ripple. This work proposes an efficient procedure to design nearly-perfect reconstruction CMFBT prototype filters with peak-constrained least-squares characteristics using a modified weighted least-squares algorithm. Substantial flexibility is added in the design of the magnitude response of the prototype filter, ranging from minimum stopband energy to minimum stopband ripple, which may be required in many applications. Some constraints are imposed to the CMFBTs in order to control the direct transfer and aliasing distortion functions, related to the intercarrier and intersymbol interferences. Algebraic simplifications are also provided on the overall objective function and associated constraints, leading to substantial reduction on the computational burden of the optimization process. The procedure is proven to be very powerful in designing CMFBT systems satisfying multiple constraints as indicated by numerical examples.     

Subspace approach for the design of cosine-modulated filter bankswith linear-phase prototype filter

A method for designing perfect reconstruction (PR) prototypes for paraunitary cosine-modulated filter banks is presented. The design procedure is based on a subspace approach that allows linear combinations of even-length linear-phase PR prototype filters in such a way that the resulting filter is also a linear-phase PR prototype. Within a given subspace, the weights of the optimal linear combination can easily be computed via an eigenanalysis. The filter design is carried out iteratively while the PR property is guaranteed throughout the design process. No nonlinear optimization routine is needed. As a special case, the proposed approach allows the design of discrete-coefficient prototypes, which are of great interest for efficient hardware implementations     

基于线性迭代的DFT调制滤波器组的设计算法

该文研究了单原型的DFT调制滤波器组的设计方法。在该方法中,滤波器组的设计问题被归结为一个无约束的优化问题,其目标函数为滤波器组的传递失真、混叠失真和原型滤波器的阻带能量的加权和。结合线性化方法,原型滤波器通过迭代求解。在单步迭代中,原型滤波器的系数通过解析式求解得到。仿真表明,与传统的设计算法相比,本文方法设计所得的DFT调制滤波器组重构误差减小了约40dB,阻带衰减提高了约2dB。并且新算法的计算复杂度明显低于传统算法。     

二阶锥规划方法对于低群延时复系数有限冲激响应数字滤波器优化设计

针对低群延时复系数有限冲激响应数字滤波器优化设计问题,提出了一种幅度和相位独立约束的等纹波设计新方法.该方法在相位误差一定的条件下对幅度的上界和下界分别采取复数圆约束和线性不等式约束,不仅提高了幅度约束的精度,而且将非凸的滤波器设计问题转化为二阶锥规划问题;同时,为抑制通带边缘附近较大的群延时震荡效应,引入了相位误差一...     

余弦调制滤波器组的原型滤波器设计

该文提出了一种近似重构的余弦调制滤波器组的原型滤波器设计方法。该方法将原型滤波器表示成A(z2)B(z)的形式(其中B(z)是最平坦FIR滤波器),通过优化低阶FIR滤波器A(z)的通带边缘频率,间接设计原型滤波器。文中给出的设计例子表明,该方法可获得很高阻带衰减的滤波器组。     

Minimax design of two-channel low-delay perfect-reconstruction FIRfilter banks

The authors deal with the design problem of low-delay perfect-reconstruction filter banks for which the FIR analysis and synthesis filters have equiripple magnitude response. Based on the minimax error criterion, the design problem is formulated in such a manner that the coefficients for the FIR analysis filters can be found by minimising the weighted peak error of the designed analysis filters, subject to the perfect-reconstruction constraints. A design technique based on a modified dual-affine scaling variant of Karmarkar's (1989) algorithm, in conjunction with approximation schemes, is then developed for solving the resulting nonlinear optimisation problem. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Design of face-centred orthorhombic filter banks

In this paper, a method to design the two-channel FIR linear-phase (LP) face-centred orthorhombic (FCO) filter banks with equiripple magnitude responses and perfect-reconstruction (PR) is presented. The necessary conditions of lengths of LP FCO filter banks satisfying the PR constraint are derived. An interior-point algorithm is utilized to optimize the peak ripples of the analysis filters and a first-order approximation skill is introduced to satisfy the PR constraint. The simulation example is presented to illustrate the effectiveness of this proposed design technique.     

Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived.     

非视距环境下基于二阶锥规划的RSS定位算法

针对无线传感器网络在非视距(NLOS)环境下利用接收信号强度(RSS)定位存在精度不足的问题,提出了一种新的基于二阶锥规划(SOCP)的鲁棒性定位算法。在假定非视距偏差上界的基础上构建了对非视距偏差量具有鲁棒性的定位方程,从而抑制了非视距偏差的干扰;接着利用凸优化技术将鲁棒性的定位问题转化为二阶锥规划问题,达到精确估计的目的,进而提高定位精度;此外,将定位问题推广到未知发射功率的情况,提出了一个迭代SOCP的算法。仿真结果表明,所提出的算法有效地解决了非视距定位中存在的问题,且定位精度要优于以往的牛顿迭代法、UT法以及SOCP法。     

Efficient design method of cosine-modulated QMF banks satisfying PR property

In this paper the design problem of perfect-reconstruction cosine-modulated QMF banks has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the QCLS optimization problem are symmetric and positive definite. A cost function which is a convex function of desired prototype filter coefficients is constructed so that this kind of QCLS optimization problems can be efficiently solved. So a global minimizer of this problem can be easily obtained. Results of two design examples are presented to support the derivations and analyses.     

基于第二代电流传输器的二阶带通滤波器设计

设计了一种单端输入单端输出的电流模式带通滤波器,核心部件为用三极管设计的第二代电流传输器（CCⅡ）.电路由两个CCⅡ和一些无源器件构成,通过偏置电流控制其中心频率,实现对信号的带通滤波功能.该滤波器提供了更大带宽下的更高电压增益,解决了电压跟随不理想的问题,且具有更低的无源灵敏度,能广泛应用于无线通讯、射频等高频模拟电路中.使用Hspice软件仿真分析并验证了理论设计的准确性和可行性.     

Multidimensional perfect reconstruction filter banks: an approach of algebraic geometry

In image compression and some other applications, multidimensional filter banks are gaining their popularity due to the decrease in implementation cost. In this article, we study these filter banks from a viewpoint of algebraic geometry, where some insights are emerging. Familiar properties, such as perfect reconstruction and linear phase, appear differently when studied from this new angle. For the sake of practicability and a better understanding of problems, our focus in this work is further restricted to the filter banks that can achieve linear phase and perfect reconstruction properties. According to different symmetry nature, the filter banks are categorized into two types. Filters in a multidimensional filter bank represented by multivariate polynomials have common zeros that are different in nature from their 1D counterparts. In this work, the relation between the above-mentioned properties and various zeros is investigated. A criterion to test such filter banks is proposed and this criterion is also interpreted in resultant theory. Based on these results, as well as a proposed conjecture, a factorization of lifting scheme is presented for one type of these filter banks. For the other type of filter banks, we propose a method on perfect reconstruction completion.

A joint TDOA and FDOA estimation algorithm based on second-order cone programming

ABSTRACT

Considering the low estimation accuracy of the traditional interpolation method, this paper, on the basis of second-order cone programming (SOCP), proposes a novel joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation interpolation method, which can attain the sub-sample precision. The proposed method uses several discrete samples produced by cross ambiguity function (CAF) to structure the convex optimization models with regard to the interpolation surface. Then, the SOCP is utilized to obtain the interpolation surface which matches the discrete surface of CAF well. Finally, the method achieves the precision superior to the traditional TDOA and FDOA estimation directly through the search for the maximum of the continuous approximate surface. This method decreases the computational load without loss of precision and can efficiently reduce the limitation of finite sampling interval and sampling time in estimation precision. Numerical simulations show that the method in this paper is efficient and outperforms existing interpolation algorithms about estimation precision.     

Design of filter banks using transformation of variables: newresults

The design problem of multirate filter banks can be divided into two parts. The first part involves the issue of reconstruction errors. The second part involves the issue of designing good quality subband filters. There is a class of techniques that we refer to as transformation of variables which satisfactorily addresses the two parts of the design problem. This class of filter banks is specified by its prototype filters and transformation (kernel). It is the flexibility and relative ease in designing the kernel that enables the technique to satisfactorily address the second part of the design problem. We present two new methods of designing the kernel that will enhance the design techniques' flexibility and effectiveness. The first is the combination of the McClellan transformation and rotation operators. The second introduces and uses the concept of directional singular value decomposition (SVD)