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。     

Design of Oversampled Interleaved DFT Modulated Filter Bank Using 2Block Gauss-Seidel Method

In this paper, we present several new properties of the recently introduced interleaved DFT modulated filter bank and an efficient algorithm for designing the filter bank. The periodicity and symmetry properties of the overall transfer function and aliasing transfer functions are stated. Then the design of the filter bank is formulated into a constrained optimization problem that jointly minimizes the overall distortion and aliasing distortion subject to fixed bounds on the stopband energy, transition-band energy, and passband flatness of the prototype filters. The constrained optimization problem is solved by the 2block Gauss-Seidel method, which alternatively optimizes the analysis PF pair and the synthesis PF pair. Since the overall distortion and aliasing distortion are jointly minimized, the proposed algorithm can lead to filter banks with small reconstruction error, even when the filter banks behave with a low redundancy ratio and short PFs. The convergence of the proposed algorithm is proved. Numerical examples and comparisons with the existing method are included to demonstrate the performance of the proposed algorithm.     

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。     

Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.     

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。     

过采样DFT滤波器组的一种简单设计方法

提出了一种几乎完全重构的过采样DFT调制滤波器组的设计方法.分析和综合滤波器组采用了不同的原型滤波器,使得设计自由度大为增加.考虑滤波器组的子带混叠、输出混叠、系统失真要求,推导并给出了相应的设计算法.实验结果证明提出的方法在相同滤波器长度情况下可以得到更好的阻带衰减.     

Filterbänke mit Überabtastung

Oversampled filter banks offer more design freedom, better numerical stability, and less sensitivity to quantization noise as compared to critically sampled filter banks. These advantages come at the cost of increased computational complexity. Therefore, oversampled modulated filter banks allowing a particularly efficient implementation are of practical interest. Furthermore, in certain applications (such as image coding) it is important to have linear phase filters in all channels of the filter bank. In this paper we discuss oversampled filter banks with emphasis on cosine-modulated filter banks and linear phase filters. We establish a relation of oversampled filter banks with redundant signal expansions. We also perform an analysis of the numerical sensitivity of oversampled filter banks. The increased design freedom in oversampled filter banks is demonstrated both theoretically and by means of simulation examples. Finally, we present a unified theory of cosine-modulated filter banks.     

过采样广义调制滤波器组在B3G移动通信系统中的实现

本文在GMC-TDD-xDMA系统背景下从广义多载波并行传输的基本原理出发,讨论广义多载波调制解调的数字实现,得到多载波调制解调的广义DFT调制滤波器组实现结构,并给出了一种普遍适用的滤波器组快速实现方法.解决了DFT调制滤波器组在GMC-TDD-xDMA系统中运用时存在的问题.     

一种设计近似完全重构非均匀余弦调制滤波器组的新算法

该文提出了一种设计近似完全重构非均匀余弦调制滤波器组的新算法。针对现有合并算法中非均匀滤波器组性能无法直接控制优化的缺点,新算法把非均匀滤波器组的设计问题归纳为一个关于原型滤波器的无约束优化问题,其中目标函数是非均匀滤波器组传递失真与原型滤波器阻带能量的加权和,最后利用线性迭代算法求解该优化问题。理论分析和数值实验表明,新算法获得的非均匀余弦调制滤波器组比现有算法设计的滤波器组整体性能更佳。     

Design of M‐Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M‐channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop‐band attenuation, which is also taken care of in the proposed algorithm.     

Design of Biorthogonal Filter Banks Using a Multi-objective Genetic Algorithm for an Image Coding Scheme

In this paper, we present an optimization method based on a multi-objective Genetic Algorithm (GA) for the design of linear phase filter banks for an image coding scheme. To be effective, the filter banks should satisfy a number of desirable criteria related to such a scheme. Instead of imposing the entire PR condition as in conventional designs, we introduce flexibility in the design by relaxing the Perfect Reconstruction (PR) condition and defining a PR violation measure as an objective criterion to maintain near perfect reconstruction (N-PR) filter banks. Particularly in this work, the designed filter banks are near-orthogonal. This has been made possible by minimizing the deviation from the orthogonality in the optimization process. The optimization problem is formulated as a constrained multi-objective, and a modified Nondominated Sorting Genetic Algorithm NSGAII is proposed in this work to find the Pareto optimal solutions that achieve the best compromise between the different objective criteria. The experimental results show that the filter banks designed with the proposed method outperform significantly the 9/7 filter bank of JPEG2000 in most cases. Furthermore, the filter banks are near orthogonal. This is very helpful, especially where embedded coding is required.     

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。      

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。     

基于DFT滤波器组的低时延FPGA语音处理实现研究

提出了WOLA（Weighted Overlap-Add）并行结构的低时延DFT滤波器组的设计和FPGA实现方法.为降低系统总体时延,在综合考虑传递失真、混迭失真的基础上,将群时延引入系统目标函数,并采用非对称综合原型滤波器设计方法,提出迭代算法,实现了DFT滤波器组低时延优化设计.通过对DFT滤波器组中分析和综合功能的关键模块采用多路并行乘法、多级流水加法链设计,实现了并行的WOLA结构DFT滤波器组,降低FPGA实现的计算时延.整个设计在Xilinx公司的Zynq7020型号FPGA芯片上进行实现.PESQ测试表明,设计的DFT滤波器组能取得较好的语音质量.与串行WOLA结构的实现对比表明,在16kHz语音采样率下,并行的WOLA结构FPGA实现的总时延能降低1.192ms,其中群时延降低12%,计算时延降低29.2%.     

Two-channel IIR QMF banks with approximately linear-phase analysisand synthesis filters

Perfect linear-phase two-channel QMF banks require the use of finite impulse response (FIR) analysis and synthesis filters. Although they are less expensive and yield superior stopband characteristics, perfect linear phase cannot be achieved with stable infinite impulse response (IIR) filters. Thus, IIR designs usually incorporate a postprocessing equalizer that is optimized to reduce the phase distortion of the entire filter bank. However, the analysis and synthesis filters of such an IIR filter bank are not linear phase. In this paper, a computationally simple method to obtain IIR analysis and synthesis filters that possess negligible phase distortion is presented. The method is based on first applying the balanced reduction procedure to obtain nearly allpass IIR polyphase components and then approximating these with perfect allpass IIR polyphase components. The resulting IIR designs already have only negligible phase distortion. However, if required, further improvement may be achieved through optimization of the filter parameters. For this purpose, a suitable objective function is presented. Bounds for the magnitude and phase errors of the designs are also derived. Design examples indicate that the derived IIR filter banks are more efficient in terms of computational complexity than the FIR prototypes and perfect reconstruction FIR filter banks. Although the PR FIR filter banks when implemented with the one-multiplier lattice structure and IIR filter banks are comparable in terms of computational complexity, the former is very sensitive to coefficient quantization effects     

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。     

An efficient digital implementation of multicarrier CDMA system based on generalized DFT filter Banks

In this paper, an efficient digital implementation of multicarrier transmission scheme based on generalized discrete Fourier transform (DFT) filter banks is presented for multicarrier code-division multiple-access (MC-CDMA) systems. Generalized DFT filter banks has been traditionally discussed for very high-speed digital subscriber lines (VDSL) wireline systems, received interest also for wireless applications. The design of the generalized DFT modulated filter banks is investigated and its fast implementation is derived in the time-domain for arbitrary integer sampling rate. Through the utilization of the generalized DFT modulated filter banks, one or more subcarriers, even noncontiguous subcarriers can be easily supported by system in both uplink and downlink, which facilitates the users to access the network in a frequency-division multiple-access manner. Simulation results show that the overall bit-error-rate performance of the proposed multicarrier transmission scheme well approaches that of a single-carrier system due to the negligible intercarrier interference introduced by an appropriate design of the generalized DFT modulated filter banks.     

线性完全重构的二维滤波器组的Groebner基设计

为设计线性完全重构的二维滤波器组,引用了计算代数中的Groebner基方法,根据线性相位条件和完全重构条件,分别设计出二维滤波器组的分析滤波器和综合滤波器的多相元矩阵,给出其参数化形式。根据小波构造理论,利用所设计的分析滤波器组构造出一个对称的纯二维小波。设计结果显示了Groebner基方法的有效性,设计方法更为简单。     

一种最优去噪线性相位滤波器组的FPGA实现

格型结构是一种可以快速高效设计过采样线性相位完全重建滤波器组的方法。一旦分析滤波器组设定后,对应的综合滤波器结构也就确定,但综合滤波器组参数却有很大的灵活性,从中可以找出具有最优去噪效果的综合滤波器组,构成一个完整的滤波器组。对于求解出的具有最优去噪效果的过采样线性相位完全重构滤波器组,文中用DSP Builder在FPGA上予以实现,并用modelsim进行功能仿真。