基于过采样的混合滤波器组性能优化

模拟误差是制约混合滤波器组信号重构精度的主要原因,如何降低由模拟误差导致的分解滤波器组系数误差成为了首要问题。引入过采样技术,研究在不同过采样率下8通道混合滤波器组的性能,寻找到过采样率最优值约等于7%。在不同模拟误差下对基于过采样的混合滤波器组的性能进行仿真,结果表明,原型结构和双阶型结构的混叠值相近,但后者对模拟误差的敏感度比前者大。信号重构阶段,在最小二乘法的基础上采用频带加权法进行误差校准。在1%模拟误差内,采用7%过采样率的原型混合滤波器组相比无过采样,平均混叠值下降了约50 dB,最大混叠值下降了约94 dB。仿真验证了引入过采样的有效性。     

采用小波进行频带分割的脉冲压缩方法

针对因频带分割滤波器的不理想产生的频谱混叠、幅度以及相位失真导致子带脉压误差较大的问题,提出了一种采用小波设计的正交镜像滤波器组进行频带分割的子带脉压方法.借助小波及多分辨分析理论,利用最优频域准则设计频带分割滤波器组,消除或减小混叠失真、幅度及相位失真后,对信号进行频域分解,实现子带脉冲压缩.仿真结果表明,和传统的子带脉压方法相比,所提的脉压方法在主副瓣比方面提高了约12 dB,最大脉压误差减小了约7 dB,验证了该算法的正确性和有效性.     

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。     

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.     

基于加权最小二乘正则化方法的混合滤波器组最优化设计

模拟分析滤波器的实现误差以及数字综合滤波器有效阶数实现的设计误差造成的病态问题都将影响混合滤波器组(HFB)的重构效果.提出一种新的满足近似完美重构的基于加权最小二乘(WLS)正则化算法的IIR形式综合滤波器设计方法.该算法根据误差量二阶统计特性采用WLS算法抑制滤波器实现误差以及随机噪声等扰动因素影响,使得到的综合滤波器组频域响应解的加权误差平方和最小化,并通过Tikhonov正则化方法优化解的稳定性.提出一种IIR类型综合滤波器设计算法,并利用正则化方法优化滤波器系数,减小设计误差.该方法可应用于过采样HFB的设计.仿真结果表明该算法的有效提高系统鲁棒性和改善重构性能.     

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。     

无完全重构约束的两通道自适应FIR滤波器组设计

该文研究了在无完全重构约束情况下两通道自适应FIR无混叠滤波器组的时域设计方法。由于放松了对完全重构的约束,子带编码器的失真由系统失真和量化失真两部分构成。在整体比特数和输入过程给定的情况下,本文通过优化滤波器系数,使得子带编码器的整体失真达到最小,实现提高其编码增益的目的。后面的设计实例验证了该方法的有效性。     

类梳状补偿滤波器设计与仿真

积分梳状（CIC：cascaded integrator comb）滤波器由于具有运算速度较快,占用资源少等优点,而被广泛应用于多信号抗混叠系统中.针对传统CIC滤波器因简单级联而带来的通带失真增大和阻带衰减减小的缺陷,本文基于CIC滤波器的传递函数以及频谱特性分析,提出了一种类梳状补偿滤波器（SCC_CIC：similar to comb compensation CIC）的设计方案,根据实际需要调整参数和来满足设计要求.同时,利用多相分解技术重构滤波器结构,提升了整个系统的运行效率,且实现复杂度较低.通过MATLAB仿真实验及分析,相比N=2的同级联数的传统CIC滤波器、ISOP_CIC （interpolated second-order polynomials CIC）和SCIC （sharpening to cascaded integrator-comb）滤波器,SCC_CIC滤波器在f_s处的阻带衰减分别增加近了80dB、60dB和70dB,在f_c处分别补偿通带失真97.3%、90.1%和-2%,整个滤波器的运算量减小到1/D,滤波器的精确度基本保持一致,使得SCC_CIC能够较好地应用在抗混叠滤波系统中.     

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。     

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。     

Design of hybrid filter banks for analog/digital conversion

This paper presents design algorithms for hybrid filter banks (HFBs) for high-speed, high-resolution conversion between analog and digital signals. The HFB is an unconventional class of filter bank that employs both analog and digital filters. When used in conjunction with an array of slower speed converters, the HFB improves the speed and resolution of the conversion compared with the standard time-interleaved array conversion technique. The analog and digital filters in the HFB must be designed so that they adequately isolate the channels and do not introduce reconstruction errors that limit the resolution of the system. To design continuous-time analog filters for HFBs, a discrete-time-to-continuous-time (“Z-to-S”) transform is developed to convert a perfect reconstruction (PR) discrete-time filter bank into a near-PR HFB; a computationally efficient algorithm based on the fast Fourier transform (FFT) is developed to design the digital filters for HFBs. A two-channel HFB is designed with sixth-order continuous-time analog filters and length 64 FIR digital filters that yield -86 dB average aliasing error. To design discrete-time analog filters (e.g., switched-capacitors or charge-coupled devices) for HFBs, a lossless factorization of a PR discrete-time filter bank is used so that the reconstruction error is not affected by filter coefficient quantization. A gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation. A four-channel HFB is designed with 9-bit (integer) filter coefficients. With internal precision limited to the equivalent of 15 bits, the maximum aliasing error is -70 dB, and with the equivalent of 20 bits internal precision, maximum aliasing is -100 dB. The 9-bit filter coefficients degrade the stopband attenuation (compared with unquantized coefficients) by less than 3 dB     

Joint use of time-domain and windowed method for design of modulated DFT filter banks

A novel and efficient technique to design modulated discrete Fourier transform （DFT） filter banks is introduced in this paper. The proposed method first relaxes the limits that the synthesis filters are the time-reversed version of the analysis filters and then adopts the time domain formula of the perfect reconstruction property as the solution to design the synthesis filters. The prototype filter in analysis filter banks is designed based on Fourier-Kaiser window approach. Simulation results show that the designed filter banks approximately satisfy the perfect reconstruction with controllable reconstruction errors.     

基于加权总体最小二乘正则化方法的混合滤波器组最优化设计

模拟分析滤波器组的实现欠理想、系统噪声以及数字综合滤波器有效阶数实现所带来的系统误差均有可能造成混合滤波器组的设计出现解不稳定、无唯一解等病态问题,影响混合滤波器组的准确重构效果。本文首先给出了满足准确重构条件下,以综合滤波器组频域响应为求解变量的混合滤波器组线性求解模型。针对线性方程中系数矩阵以及目标向量受扰动误差影响特点,提出一种新的基于加权总体最小二乘正则化算法的IIR形式综合滤波器设计方法。算法以系统扰动误差最小化为目标函数,根据随机误差变量的二阶统计特性,采用加权总体最小二乘算法抑制滤波器实现误差以及随机噪声等扰动因素影响,使得到的综合滤波器组频域响应解的加权误差平方和最小化,并通过Tikhonov正则化方法优化病态情况下方程组解的稳定性。提出一种IIR类型的综合滤波器系数的求解算法,并利用正则化方法优化滤波器系数,提高系统稳定性。该方法可应用于过采样混合滤波器组的设计。仿真结果表明该算法的有效提高系统鲁棒性和改善重构性能。      

Calibration for Realization Errors of Two-Channel Hybrid Filter Bank Analog-to-Digital Converters Based on Frequency-Dependent Model

Hybrid filter bank (HFB) analog-to-digital converters (ADCs) are used to achieve higher sampling rates for medium-to-high resolution applications in many communication systems. However, the analog filter realization errors and channel mismatches severely degrade the reconstruction performance of HFB ADCs. A general error analysis, which takes analog imperfections and channel mismatches into consideration based on a single-channel filtering (SCF) HFB architecture is presented in this paper. A frequency-dependent model (FDM) for sub-ADCs output is then derived to integrate all the realization errors to an equivalent channel-transfer function (ECTF). Based on the ECTF, the perfect reconstruction condition is derived as the optimization object for the synthesis filter banks. Finally, a two-channel SCF HFB ADC prototype with 12-bit resolution and 200 MHz sampling rate is implemented. After mismatch correction with 64-tap finite impulse response (FIR) filters, 75.75 dB of spurious-free dynamic range (SFDR) is achieved over the whole bandwidth. The experimental results show that the average SFDR is enhanced by about 10–25 dB compared with the traditional calibration method.     

Time-domain design of FIR multirate filter banks

A new time-domain methodology for designing FIR multirate filter banks is proposed. The conditions for perfect reconstruction systems can only be met by a limited number of systems, and consequently one of the major problems is to design analysis and synthesis filters which reduce the reconstruction error to a minimum. A recursive technique is proposed which uses the synthesis filters from one iteration to update the analysis filters for the next. The Letter shows that this is computationally simpler than previously proposed time-domain methods and produces filter banks in which the reconstruction error is reduced to practically acceptable levels.<>     

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。      

Optimal design of nonuniform multirate filter banks

The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Design of selective M-channel perfect reconstruction FIR filterbanks

A new method is presented for the optimal design of M-channel perfect reconstruction FIR quadrature mirror filter (QMF) banks which is based on the orthogonal matrix concept. The parameters of the analysis filters are adjusted so that they have a linear phase and minimum stopband energy. Comparison with a recently published method reveals that the resulting design procedure gives better stopband characteristics. A numerical design example is included to validate the theory and to demonstrate the superiority of the designed filters from selectivity, reconstruction and distortion points of view     

Theory and design of two-parallelogram filter banks

It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow alias cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synthesis filters are cosine-modulated versions of a prototype that has a parallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB are derived     

Near-perfect-reconstruction pseudo-QMF banks

A novel approach to the design of M-channel pseudo-quadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is constrained to be a linear-phase spectral-factor of a 2Mth band filter. As a result, the overall transfer function of the analysis/synthesis system is a delay. Moreover, the aliasing cancellation (AC) constraint is derived such that all the significant aliasing terms are canceled. Consequently, the aliasing level at the output is comparable to the stopband attenuation of the prototype filter. In other words, the only error at the output of the analysis/synthesis system is the aliasing error which is at the level of stopband attenuation. Using this approach, it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of -100 dB. Moreover, the resulting reconstruction error is also on the order of -100 dB. Several examples are included