Design of linear phase M-channel perfect reconstruction FIR filterbanks

We propose two approaches to design M channel nonparaunitary filter banks that satisfy perfect reconstruction (PR) and linear phase (LP) properties. In the first approach, the PR condition is imposed on only a high-pass filter. Although this method does not require nonlinear optimization, it has a demerit in that the order of a high-pass filter becomes high. In the second approach, two filters are optimized simultaneously using a Lagrange-Newton method. We can design PR filter banks that have the same length. The PR constraint is also formulated as a linear and nonlinear equation of the analysis filter coefficients. Finally, some design examples are included     

m序列相位编码信号的最小峰值旁瓣滤波器

m序列相位编码信号最小峰值旁瓣滤波器(LP滤波器)的冲激响应序列可以通过解线性规划问题求得。对于15位和31位全部m序列的计算结果表明,LP滤波器对峰值旁瓣有较大的抑制。对[4,3,0]反馈连接的起始状态为1001的15位码,它的长度为15的LP滤波器的峰值旁瓣电平降到—21.47dB,比用匹配滤波器改善7.49dB;对[5,3,2,1,0]反馈连接的起始状态为11101的31位码,它的长度为31的LP滤波器的峰值旁瓣电平降到—23.80dB,比用匹配滤波器改善6.01dB。当滤波器的长度增加时,LP滤波器可把峰值旁瓣抑制到更低电平。     

一种全解耦的RLS自适应Volterra滤波器

本文研究了Volterra自适应滤波器解耦问题,提出了一种全解耦的RLS自适应Volterra滤波器.按照Volterra滤波器的伪线性组合结构,采用RLS滤波原理和约束优化理论,导出了满足最小累计平方误差指标的具有分块对角形输入相关矩阵的全解耦Volterra标准方程,据此设计了一种全解耦的RLS自适应Volterra滤波器,给出了滤波器权向量自适应修正的一套公式.仿真结果验证了本文方法的有效性.     

Baseband Volterra filters for implementing carrier basednonlinearities

A diagonal coordinate representation for Volterra filters is developed and exploited to derive efficient Volterra filter implementations for processing carrier based input signals. In the diagonal coordinate representation, the output is expressed as a sum of linear filters applied to modified input signals. Hence, linear filtering methods are employed to implement the nonlinear filter on a baseband version of the input. Downsampling is then used to reduce computational complexity. The same approach is employed to develop efficient implementations for processing continuous-time carrier-based signals, pulse amplitude-modulated signals, and frequency division multiplexed input signals     

图像边缘提取的自适应Volterra滤波器设计

Ｖｏｌｔｅｒｒａ滤波是研究信号高阶统计冗余性的一种有效途径。我们提出了一种用于提取图像边缘的自适应二次Ｖｏｌｔｅｒｒａ滤波器设计方法。这种滤波器是推广型Ｔｅａｇｅｒ基滤子的线性组合，其系数用基于极小化最小均方能量函数的共轭梯度法研究；它兼有局域平均和高通特性，因而可均衡去除噪声和增强图像边缘。文章还给出了计算实例。     

On characterization of linear phase nonuniform filter banks

In this paper, a condition termed as linear phase condition (LPC), which ensures that the filters of a nonuniform filter bank are linear phase, is presented. It is observed that the proposed LPC is also applicable to the uniform filter bank case. Further, the utility of this LPC to find (i) necessary restrictions on the filters lengths, (ii) the number of symmetric and antisymmetric filters in the filter bank and (iii) filter bank decimation factors is also investigated. The results obtained for the different cases are also presented in the form of tables. These tables will facilitate the design of nonuniform filter bank by ruling out the non-solvable cases and by reducing the search space, thus saving the designers’ precious time.     

SAW 15位m序列相位编码信号的最小峰值旁瓣滤波器

本文介绍用线性规划方法求解[4,3,0]反馈连接的、起始状态为1001的15位m序列相位编码信号的最小峰值旁瓣滤波器(LP滤波器)的计算结果。长度为15的LP滤波器的峰值旁瓣电平降到－21.47dB,比匹配滤波器改善7.49dB,当滤波器的长度增加时,LP滤波器可把峰值旁瓣抑制到更低电平。并介绍用声表面波(SAW)技术制作15位m序列相位编码信号(起始状态为1001)的LP滤波器,实验结果,其峰值旁瓣电平为－19dB,与理论值相差2.47dB。     

Saw minimum peak sidelobe filter for 15-bitM-sequence phase code signals

This paper presents computation results of the minimum peak sidelobe filter (LP filter) for the 15-bitM-sequence phase coded signal with feedback connection [4,3,0] and initial condition 1001. The design of the filter resorts to the linear programming method. The peak sidelobe level is reduced to −21.47 dB by the LP filter of length 15, and is 7.49 dB lower than that by the matched filter. The LP filter can suppress the peak sidelobe even more by increasing its length. The minimum peak sidelobe filter for the 15-bitM-sequence phase coded signal (initial condition 1001) has been implemented with a surface acoustic wave (SAW) device. Experiments show that the peak sidelobe level of the manufactured filter is −19 dB and, thus, only differs from the theoretical value of −21.47 dB by 2.47 dB.     

Geometrical properties of optimal Volterra filters for signaldetection

Linear-quadratic filters are a special example of Volterra filters that are limited to the second order. It is shown that all the results recently published which are valid in the linear-quadratic case can be extended with the appropriate notations to Volterra filters of arbitrary order. Particularly, the optimum Volterra filter giving the maximum of the deflection for detecting a signal in noise is wholly calculated. In addition, several geometrical properties of optimal Volterra filters are investigated by introducing appropriate scalar products. In particular, the concept of space orthogonal to the signal and the noise alone reference (NAR) property are introduced, allowing a decomposition of the optimal filter that exhibits a relation between detection and estimation. Extensions to the infinite case and relations with the likelihood ratio are also investigated     

Equivariant holomorphic filters for contour denoising and rapid object detection.

It is well known that linear filters are not powerful enough for many low-level image processing tasks. However, it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are, at the same time, equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant nonlinear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results. The relations of the proposed approach to Volterra filters and steerable filters are shown. In the context of detection problems, the filter may be interpreted as some kind of generalized Hough transform. The experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images. In the detection context, our experiments show that the proposed filter is definitely superior to alternative approaches, when high localization accuracy is required.     

Design of linear combination of weighted medians

This paper introduces a novel nonlinear filtering structure: the linear combination of weighted medians (LCWM). The proposed filtering scheme is modeled on the structure and design procedure of the linear-phase FIR highpass (HP) filter in that the linear-phase FIR HP filter can be obtained by changing the sign of the filter coefficients of the FIR lowpass (LP) filter in the odd positions. The HP filter can be represented as the difference between two LP subfilters that have all positive coefficients. This representation of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a nonlinear HP filter that is commonly used in edge detection. Based on this observation, we introduce a class of LCWM filters whose output is given by a linear combination of weighted medians of the input sequence. We propose a method of designing the 1-D and 2-D LCWM filters satisfying required frequency specifications. The proposed method adopts a transformation from the FIR filter to the LCWM filter. We show that the proposed LCWM filter can offer various frequency filtering characteristics including “LP,” “bandpass (BP),” and “HP” responses     

Tensor product basis approximations for Volterra filters

The paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, it is often highly overparameterized. Due to the large number of parameters, the utility of the Volterra filter is limited. The overparameterization problem is addressed in the paper using a tensor product basis approximation (TPBA). In many cases, a Volterra filter may be well approximated using the TPBA with far fewer parameters. Hence, the TPBA offers considerable advantages over the original Volterra filter in terms of both implementation and estimation complexity. Furthermore, the TPBA provides useful insight into the filter response. The paper studies the crucial issue of choosing the approximation basis. Several methods for designing an appropriate approximation basis and error bounds on the resulting mean-square output approximation error are derived. Certain methods are known to be nearly optimal     

A Novel Adaptive Nonlinear Filter-Based Pipelined Feedforward Second-Order Volterra Architecture

Due to the computational complexity of the Volterra filter, there are limitations on the implementation in practice. In this paper, a novel adaptive joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) to reduce the computational burdens of the Volterra filter is proposed. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the feedforward second-order Volterra (SOV), and a linear combiner performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear and linear combiner subsections, respectively. Moreover, the analysis of theory shows that these adaptive algorithms based on the pipelined architecture are stable and convergence under a certain condition. To evaluate the performance of the JPPSOV, a series of simulation experiments are presented including nonlinear system identification and predicting of speech signals. Compared with the conventional SOV filter, adaptive JPPSOV filter exhibits a litter better convergence performance with less computational burden in terms of convergence speed and steady-state error.     

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

$M$th-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat$R$-regular finite impulse response (FIR)$M$th-band filters with a specified integer group delay at$ omega =0 $is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat$R$-regular FIR$M$th-band filters via the blockwise waveform moments. Differing from the conventional FIR$M$th-band filters with exactly linear phase responses, the generalized FIR$M$th-band filters proposed in this paper have an arbitrarily specified integer group delay at$ omega =0 $. Moreover, a new efficient implementation of the generalized maxflat$R$-regular FIR$M$th-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR$M$th-band filters.     

UFMC系统中基于Volterra滤波器的非线性失真补偿方案

为实现通用滤波多载波(UFMC)通信系统高效、可靠的通信性能,需在最大程度上补偿由记忆型高功率放大器(HPA)引起的非线性失真.为解决HPA造成的失真问题,本文提出了一种基于Volterra滤波器的非线性失真补偿(V-NLDC)技术.该技术利用了Volterra级数的稀疏特性和能够模拟任意精度非线性系统的性质以逐次逼近的方式对信号进行预失真.将预失真后的信号传送至HPA,然后采用噪声消除器做进一步噪声消除处理,以达到更小失真度的目的.同时,本研究采用收敛速度快、性能稳定的自适应最小二乘法(RLS),可根据环境变化自适应地计算Volterra滤波器和噪声消除器的系数.通过大量蒙特卡罗仿真实验证实了所提出的非线性失真补偿技术可以很好的补偿由记忆型HPA非线性失真所造成的影响,从而优化系统性能.     

Digital transmission performance of standard analog filters

This work analyzes the performances of Bessel, Gaussian, Butterworth, and Chebyshev (0.1-dB ripple) filters for synchronous baseband digital transmission. Numerical results showing the effects of system parameters such as signal rate, filter bandwidth, filter order, and pulse duty-cycle are presented. For rectangular inputs, linear phase filters perform better than those with nonlinear phase, from the viewpoint of the Nyquist 1 criterion. In terms of the Nyquist 2 criterion, linear phase filters perform better when the input duty-cycle is unity. For lower duty-cycles, there are symbol rate ranges over which nonlinear phase filters perform better. From the viewpoint of symbol time synchronization, the performances of the two types of filter are essentially the same. Linear phase filters are more robust to sampling clock jitter than nonlinear ones when the symbol rate is higher than the bandwidth. Furthermore, it is shown that for linear phase filters it is possible to increase the transmitting rate while keeping the filter bandwidth constant and with only a minor increase in degradation, by using low duty-cycle inputs     

Nonlinear adaptive bilinear filters for active noise control systems

The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.     

Design of 2D oversampled linear phase DFT modulated filter banks via modified Newton's method

In this paper, the structure of the 2D oversampled DFT modulated filter banks is analyzed and a spatial-domain condition of a filter bank without transfer function distortion is derived. Based upon the spatial-domain condition, a modified Newton's method is presented for fast design of 2D oversampled linear phase (LP) DFT modulated filter banks with nearly perfect reconstruction (NPR). We formulate the design problem into an unconstrained optimization with a fourth-order objective function, which is the weighted sum of the transfer function distortion of the filter bank and the stopband energy of the prototype filter (PF). The optimization is solved by the modified Newton's method, where each of iterations updates the PF by a set of linear equations. It is proved that the iteration process fast converges to a stationary point of the objective function. Compared with the existing methods, the new method is fast in computation and can design 2D filter banks with a large number of subbands.     

Linear phase paraunitary filter banks: theory, factorizations anddesigns

M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. The authors study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. They begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, they develop a minimal factorization for a large class of such systems. This factorization will be proved to be complete for even M. Further, they structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. They then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory