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。     

用频障法设计高效FIR滤波器

介绍了多载波通信中一种设计高效宽带锐截止FIR(有限冲击响应)滤波器的新方法———频障法。通过选择特定的原型滤波器来降低实现宽带锐截止FIR滤波器的复杂度。首先设计一个合适的宽带低通原型FIR滤波器Ha(z),然后得到其互补滤波器Hc(z)。再对它们进行L倍内插,得到两个互补的多带滤波器Ha(zL)、Hc(zL),然后用合适的频障滤波器HMa(z)和HM c(z)分别去消除Ha(zL)、Hc(zL)中不需要的频带,相应的输出加在一起就是所要设计的滤波器H(z)。详细研究了该方法的实现结构和设计方法,并通过设计实例证明了实现同样的性能时频障法比其他方法能节省很大的运算量,因而具有较高的应用价值。     

基于QPSO算法的准完全重构余弦调制滤波器组的优化设计

提出了一种准完全重构的余弦调制滤波器组的设计方法,使用优化方法设计原型滤波器。该方法固定原型滤波器的阻带截止频率为ωs=π/M,以通带截止频率ωp为参数变量,用量子粒子群优化算法(QPSO)优化满足重构条件的目标函数,间接设计原型滤波器,然后通过调制得到余弦调制滤波器组。稍微放宽余弦调制滤波器组的精确条件,从而大大降低了设计的复杂性,减少运行时间。仿真实验结果表明,该算法简单有效,可获得具有高阻带衰减、低混叠误差和重构误差的余弦调制滤波器组。     

M带余弦调制滤波器组的迭代设计算法

余弦调制滤波器组的设计问题通常是关于原型滤波器系数的非凸优化问题,设计的优劣很大程度上取决于设计问题的归结和所采用的求解算法.本文提出了一种基于迭代的设计方法,用于设计近似完全重构的余弦调制滤波器组.该方法通过松弛完全重构条件和运用迭代的思想,将余弦调制滤波器组的设计归结为一个易于求解的优化问题.在该优化问题中,原型滤...     

二维双原型完全过采样DFT调制滤波器组的快速设计方法

传统的2维大规模滤波器组的设计方法具有复杂度高的缺点。该文提出一种设计2维双原型滤波器组的快速方法,该方法利用近似完全重构的条件,并采用完全过采样的离散傅里叶变换(DFT)调制滤波器组来设计。新算法将两个原型滤波器的设计问题归结为一个无约束优化问题,其中目标函数为滤波器组的总体失真(传递失真和混叠失真)与原型滤波器阻带能量的加权和,利用目标函数的梯度向量,通过双迭代机制求解该优化问题。单步迭代中,利用矩阵求逆的等效条件和块Toeplitz矩阵求逆的快速算法,显著地降低了计算复杂度。理论分析和数值实验表明,新算法可以得到整体性能更好的滤波器组,计算复杂度大幅度降低,故可以快速设计大规模的2维滤波器组。     

一类冗余比为2的二维DFT调制滤波器组的设计

本文构建了一类冗余比为2的二维线性相位的双原型离散傅立叶变换（DFT）调制滤波器组。利用原型滤波器的多相位分解,推导出了该滤波器组的完全重构(PR)条件。基于该PR条件,我们将滤波器组的设计归结为一个关于原型滤波器的多相位分量的无约束优化问题。由于原型滤波器是线性相位的,多相位分量之间具有一定的关系,因此我们可以简化该优化问题。仿真结果验证了滤波器组PR条件的正确性。同时,仿真表明了优化算法的有效性,设计所得的滤波器组重构误差很小、频率特性较好,基本满足实际应用的需要。      

准完全重构余弦调制滤波器组的最优化设计

提出一种准完全重构(NPR)余弦调制滤波器组(CMFBs)的最优化设计方法.通过使用最优化方法设计原型滤波器,使其过渡带具有平方根余弦滚降(SRCR)特性.这种原型滤波器能够更好地满足设计NPR CMFBs所需的平坦性条件.CMFBs设计问题的核心被归结为一个凸极小极大最优化问题,可以用二阶锥规划(SOCP)算法进行求解.该设计方法不需要用户提供原型滤波器的初始值,并且在滤波器阶数和过渡带宽一定的情况下能获得更小的重构误差和更大的阻带衰减.     

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。     

具有重构特性的原型滤波器的设计

针对传统单参数优化法设计的原型低通滤波器存在设计复杂,性能不理想的问题,提出了一种利用窗函数截取平方根升余弦函数获取滤波器系数的设计方法。该方法将具有功率互补特性的平方根升余弦函数作为原型函数,通过迭代算法来确定滤波器长度,进而利用窗函数设计原型低通滤波器。仿真结果表明,该方法设计的原型滤波器的阻带衰减达到了-116dB,滤波器组的重构误差在5×10-4dB以内,性能优于传统单参数法设计的滤波器组,具有良好的重构特性。     

双原型离散傅里叶变换调制滤波器组的快速设计方法

针对大规模的离散傅里叶变换(DFT)调制滤波器组设计算法复杂度高的问题,该文提出一种基于无约束优化的快速设计算法。该算法将两个原型滤波器的设计问题归结为一个无约束优化问题,将滤波器组的传递失真,混叠失真以及原型滤波器阻带能量的加权和作为目标函数。进而,采用双迭代机制来求解该优化问题。在单步迭代中,运用矩阵求逆的等效条件和Toeplitz矩阵求逆的快速算法,显著地降低了迭代的计算代价。仿真对比表明,与已有的设计算法相比,新算法计算代价低 ,可以得到整体性能更好的滤波器组,并且可以快速设计大规模的滤波器组。     

On the design of FIR analysis-synthesis filter banks with highcomputational efficiency

Presents an effective design algorithm for analysis-synthesis filter banks with computationally efficient structures. Although a wide variety of implementation structures can be accommodated, the focus of the paper is on cosine modulated filter banks. The design procedure is based on a time domain formulation of analysis-synthesis filter banks in which each individual channel filter is constrained to be a cosine modulated versions of a baseband filter. The resulting filter banks are very efficient in terms of computational requirements and are relatively easy to design. A unique feature of this approach is that relatively low reconstruction delays can be imposed on the system. A discussion of the associated computational properties of the designed systems and some design examples are included     

Time-domain modified DFT modulated filter banks for multi-carrier transceiver systems

A time domain designing method is proposed for discrete Fourier transform （DFT） modulated filter banks （DFT-FBs） for application in multi-carrier transceiver systems. Instead of using the time-reversed pair limitation between the transmitting /receiving filter pair, the receiving filters in the proposed filter banks are derived from transmitting filters in accordance with the Moore-Penrose generalized inverse matrix. It can be freely obtained to design the transmitting prototype filter, which mainly affects the level of spectral containment. Furthermore, the symbol error rate （SER） performance of the proposed filter bank based trans-multiplexer with one tap equalizer is investigated in ideal channel and multi-path channel environments respectively. Simulation shows that the proposed approach can achieve significant SER reductions when square root raised cosine （RRC） prototype filter is used for comparing with the orthogonal frequency division multiplexing （OFDM） and the general DFT-FBs based applications.     

利用频率掩蔽法设计均匀和非均匀余弦调制滤波器组

给出了一种均匀非均匀余弦调制滤波器组的设计方法。采用了频率掩蔽法设计原型滤波器,利用迭代算法优化原型滤波器的脉冲响应系数,目标函数表示为脉冲响应系数的四次方,非均匀余弦调制滤波器组通过合并均匀余弦调制滤波器组的相邻的滤波器得到,这种方法简单有效。最后的Matlab实例仿真验证了此算法的有效性。     

滤波器组在相干激光测风雷达信号处理中的应用

首先简要介绍了相干激光测风雷达和数字滤波器组的工作原理,然后重点分析了余弦调制滤波器组。余弦调制滤波器组具有实现简单、占用资源少等特点。信号通过滤波器组后可分解成若干个窄带子信号,目标的多普勒频率将落入其中一个子带信号中,针对这一子信号进行处理可获得较高的信噪比。利用Matlab设计出了8通道余弦调制滤波器组,然后对回波信号进行处理,从仿真结果和实测信号处理结果可以看出:该方法可以判断并抽取出多普勒频率所在的子带信号。     

A general formulation of modulated filter banks

This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complex-modulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation-modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization)     

用于宽带接收的近似完全重构滤波器组的改进设计

本文提出了一种可用于宽带接收信号近似完全重构的余弦调制滤波器组。首先将滤波器组的设计转化为原型滤波器的设计,利用代价函数保证其通带平稳和阻带衰减,针对已有算法中幅度失真较大的问题,文中利用代价函数保证过渡带具有平方根余弦滚降特性,并且为了避免加强目标函数约束所带来的误差,对通带截止频率进行调整使得原型滤波器的3dB通带截止频率等于理想滤波器的通带截止频率。文中还推导了以滤波器系数为变量,代价函数的闭合解表达式,并针对滤波器设计复杂度高的问题,采用了基于迭代求解原型滤波器的方法。实验仿真表明,该方法得到的调制滤波器组较已有设计方法具有更好的性能。      

Symmetric delay factorization: generalized framework forparaunitary filter banks

The symmetric delay factorization (SDF) was introduced to synthesize linear-phase paraunitary filter banks (LPPUFBs) with uniform order (i.e., filter length equal to NM for arbitrary N) and real-valued coefficients. The SDF presents the advantage of decomposing the polyphase transfer matrix (PTM) into only orthogonal matrices, even at the boundary of finite-duration signals, simplifying significantly the design of time-bounded filter banks (TBFBs) or of time-varying filter banks (TVFBs). However, the symmetric delay factorization applies only to LPPUFBs. On the other hand, lattice structures, as well as finite-size lattice structures, are proposed for classes of nonlinear-phase paraunitary filter banks, as the modulated lapped transform (MLT) and the extended tapped transform (ELT). This paper describes a new minimal and complete symmetric delay factorization valid for a larger class of paraunitary filter banks, encompassing paraunitary cosine modulated filter banks, with nonlinear phase basis functions, as well as for a set of LPPUFBs including the linear-phase lapped orthogonal transforms (LOTs) and the generalized tapped orthogonal transforms (GenLOTs). The derivations for filter banks with even and odd numbers of channels are formulated in a unified form. This approach opens new perspectives in the design of time-varying filter banks used for image and video compression, especially in the framework of region or object-based coding