不确定观测下线性最小均方误差估计量的递推算法

对于在不确定观测下的线性离散时间系统,在递推线性最优估计量存在的情况下,本文导出了线性最优滤波器与一步预报器的一种递推公式。     

基于FPGA的FIR滤波器高效实现

本文针对在FPGA中实现FIR滤波器的关键--乘法运算的高效实现进行研究,首先给出了将乘法转化为查表的DA算法,然后简要介绍整数的CSD表示和我们根据FPGA实现要求改进的最优表示;接着,本文讨论了在离散系数空间得到FIR滤波器系数最优解的混合整数规划方法;最后采用这一方法设计了最优表示离散系数FIR滤波器,通过FPGA仿真验证这一方法是可行的和高效的.     

用于信号逼近的最佳正交子波选择方法

离散子波变换将离散时间信号分解为一系列分辨率下的离散逼近和离散细节。紧支的正交规范子波与完全重建正交镜象滤波器组相对应。本文提出一种用于信号最佳逼近的正交子波选择方法,即选择满足一定条件的滤波器的方法。通过对滤波器参数化,可以将带约束的最优化问题转化为无约束最优化问题,通过对参数在一定范围内的搜索,得到最优解。文中给出了计算机模拟的结果。     

基于GUI的数字信号处理课程演示系统研究

MATLAB中的Guide是专用于图形用户界面的快速开发环境,利用该Guide工具可以辅助数字信号课程教学。文章设计了基于GUI的数字信号处理课程演示系统,该系统可以登录界面,共有7块,分别开发了离散时间信号设计、离散时间系统设计、离散线性卷积设计、离散傅里叶变换设计、离散时间信号的傅里叶变换、系统频率响应设计,FIR数字滤波器的设计和IIR数字滤波器的设计。其中我们重点设计了离散卷积和滤波器设计演示系统。此系统可以辅助课堂教学,即便不懂MATLAB语言编程的人也很容易理解和掌握,享受画面的动态感,提高其对这方面的学习兴趣。     

用于信号逼近的最佳正交子波选择方法

离散子波变换将离散时间信号分解为一系列分辨率下的离散逼近和离散细节，紧支的正交规范子波与完全重建正交镜象滤波器组相对应。本文提出一种用于信号最佳逼近的正交子波选择方法，即选择满足一定条件的滤波器的方法。通过对滤波器参数化，可以将带约束的最佳化问题转化为无约束最优化问题，通过对参数在一定范围内的搜索，得到最优解，文中给出了计算机模拟的结果。     

基于自适应优化的经验数据分解滤波器的设计

对经验数据分解算法进行了研究,从滤波器完全重构出发,研究了经验数据分解滤波器与两通道滤波器组对应滤波器参数的关系,得出分析和综合滤波器都为FIR滤波器应满足的条件.可根据不同的应用对分析高通滤波器进行灵活地设计,并保证重建滤波器是FIR滤波器.利用离散线性定常系统的最优滤波和预测技术对分析高通滤波器的系数进行了预测,使用超光谱图像数据进行测试分析,确定了最佳预测滤波器的系数.结合JPEG2000的核心算法EBCOT对超光谱图像数据进行处理,并比较了该算法的输出码率同JPEG2000中无损压缩输出码率.结果表明经验数据分解算法产生的图像输出码率比JPEG2000中无损压缩输出码率平均小0.217bpp,是一种对非平稳数据有效的分析方法.     

一类非线性时滞系统的鲁棒H∞滤波器设计

 研究了满足下列条件的时滞系统的鲁棒H_∞滤波问题:假设系统的参数矩阵带有不确定性,且不确定参数是时变且范数有界的.在系统的状态与输出中同时都含有非线性无穷分布时滞与离散时滞.在设计滤波器的过程中,引入了一个新的Lyapunov-Krasovskii泛函.通过线性矩阵不等式技术,提出了参数不确定时滞系统的鲁棒H_∞滤波器存在的时滞依赖条件.鲁棒H_∞滤波器可以保证带有参数不确定性的滤波误差系统是渐近稳定的,并且满足给定的H_∞性能指标.通过仿真的研究证明了该方法的有效性.     

二维半平面线性相位FIR数字滤波器的最小二乘设计方法

本文研究了二维线性相位实系数FIR数字滤波器的最小二乘设计问题，导出了滤波器系数的闭式解。运用给出的计算公式可方便地计算滤波器的系数，而不必对矩阵进行数值求逆运算也不需要复杂的优化过程．设计实例表明本文给出的方法程序简单、计算时间极短．     

渐进扩展卡尔曼滤波器

渐进贝叶斯方法将贝叶斯更新步骤等效为伪时间上的连续演化过程,以实现对状态的后验估计.本文基于渐进贝叶斯框架,导出一种新的高斯型非线性滤波算法.在线性高斯条件下推导了渐进贝叶斯方法的精确解;证明了对于由线性高斯解确定的动态系统,其均值和协方差矩阵满足的微分方程与常数状态估计的Kalman-Bucy滤波器是一致的.对于非线性系统,利用一阶Taylor展开推导了近似解表达式,进而导出渐进扩展卡尔曼滤波器.仿真算例表明新滤波器性能较扩展卡尔曼滤波器有大幅提高,且避免了窄形似然函数带来的滤波性能恶化问题.     

一种三阶Volterra自适应滤波算法

采用更高阶Volterra滤波器更好地逼近非线性系统时,Volterra自适应滤波算法的计算复杂度呈幂级数增加。针对此问题,本文提出了一种在α稳定分布噪声背景下基于离散余弦变换(DCT)的三阶Volterra滤波算法。首先将Volterra滤波器的三次项权系数矩阵分解成一组二次项权系数矩阵;然后利用正交变换,将二次项权系数矩阵变换成对角矩阵,从而大大减少了权系数个数,有效降低了算法的计算复杂度;最后将Volterra自适应滤波器输出表示成线性滤波器输出形式,并由此得到权系数自适应调整算法。系统辨识的仿真结果表明,本算法在α稳定分布噪声背景下具有优越的性能。     

过程噪声未知但有界情况下系统最优滤波器设计方法

本文基于模型匹配方法提出了一种极小化误差幅值的线性系统的最优滤波器的设计方法,所考虑的过程噪声和量测噪声均为未知但幅值有界信号.该方法的特点是能够处理无穷观测数据量的最优滤波问题.当系统的初始条件已知时,将滤波器设计问题化为一个标准二块₁优化问题;当系统含有未知但有界初始条件时该问题归结为有限个标准₁优化问题,而标准₁优化问题已有成熟算法求解.仿真实例子说明了所提出方法的有效性和可行性.     

Robust filtering for discrete-time systems with saturation and its application to transmultiplexers

This paper considers the problem of robust filtering for discrete-time linear systems subject to saturation. A generalized dynamic filter architecture is proposed, and a filter design method is developed. Our approach incorporates the conventional linear H/sub 2/ and H/sub /spl infin// filtering as well as a regional l/sub 2/ gain filtering feature developed specially for the saturation nonlinearity and is applicable to the digital transmultiplexer systems for the purpose of separating filterbank design. It turns out that our filter design can be carried out by solving a constrained optimization problem with linear matrix inequality (LMI) constraints. Simulations show that the resultant separating filters possess satisfactory reconstruction performance while working in the linear range and less degraded reconstruction performance in the presence of saturation.     

一类非线性时滞离散系统模糊H∞滤波器的设计

本文针对一类非线性、多时滞、干扰有界未知的离散系统进行H_∞模糊滤波器的设计.首先,利用T-S模糊模型来表达这个非线性、多时滞系统,并将建模误差,通过S-procedure,考虑到滤波器的设计中,建立基于T-S模糊模型的滤波器的存在条件,降低了滤波器设计的保守性.然后根据线性矩阵不等式(LMI)的性质将该模糊滤波器的设计转化为LMI的可行性问题,并采用凸优化技术的内点法求得LMI的可行解,设计出模糊滤波器.仿真结果表明,该方法是有效的.     

Envelope-constrained H2 FIR filter design

In this paper, we consider an envelope-constrained (EC)H ₂ optimal finite impulse response (FIR) filtering problem. Our aim is to design a filter such that theH ₂ norm of the filtering error transfer function is minimized subject to the constraint that the filter output with a given input to the signal system is contained or bounded by a prescribed envelope. The filter design problem is formulated as a standard optimization problem with linear matrix inequality (LMI) constraints. Furthermore, by relaxing theH ₂ norm constraint, we propose a robust ECFIR filter design algorithm based on the LMI approach.     

High-speed and high-precision motion control with an optimal hybrid feedforward controller

An optimal feedforward controller which makes a hybrid usage of the shift (q) and delta (/spl delta/) operators is proposed for high-speed and high-precision digital motion control systems. Uncancellable discrete-time zeros arising from sampling the continuous-time plant at high rates, which make the mathematical inverse unstable, are handled in a natural way. The controller is optimized to have good performance in both low and high frequency ranges, and it is able to handle uncancellable discrete-time zeros in the right half plane. The optimization problem is generalized to an H/sup /spl infin// problem. Convex minimization is used to find the solution to the optimization problem. Simulation results and experiments carried out on an MC-510V Matsuura vertical machining center show superior performance of the proposed optimal hybrid feedforward controller.     

Robust Fault Detection of Markovian Jump Systems

This paper deals with the problem of observer-based robust fault detection for both continuous- and discrete-time linear Markovian jump systems with an unknown input. By using a fault detection filter as residual generator and a proposed performance index as objective function, the robust fault detection filter design is formulated as an optimization problem. A sufficient condition to solve this problem is established in terms of the feasibility of certain matrix inequalities, which can be solved via iterative linear matrix inequality (LMI) algorithms. The residual evaluation problem is also considered. A numerical example is given to illustrate the effectiveness of the proposed techniques.     

最小误差空域预滤波矩阵求解及误差分析

建立了空域矩阵滤波器设计最优化问题,利用两种方法给出该最优化问题的最优解。第一种方法是通过将最优化问题转化为以向量为未知数的另一个最优化问题,并求解稳定点,重排获得原问题的最优解。第二种方法是利用对原最优化问题求偏导数的方式,直接获得最优解。利用广义奇异值分解,给出了最优解的简化形式。通过仿真,给出了不同阵元数情况下,预滤波的响应效果,通过对比可知,与恒定阻带抑制滤波器相比,最小误差空域预滤波矩阵有更小的归一化响应误差。     

Decentralized Optimal Fusion Filtering for Multi-Sensor Multi-Delay Singular Systems

The optimal fusion problem for the state estimation of discrete-time multi-sensor multi-delay stochastic singular systems is considered. The key idea is to convert a multi-sensor stochastic singular system into a group of nonsingular systems. Applying projection theory, the state estimation and estimating error variance for each local nonsingular subsystem are derived. After obtaining the estimating error cross-covariance between local subsystems, and using the optimal fusion algorithm in the linear minimum variance sense, a fusion filter for the original singular system is derived. A simulation example shows that the fusion filter is better than each local filter.     

Deconvolution filter design via l1 optimizationtechnique

A new l₁ optimal deconvolution filter design approach for systems with uncertain (or unknown)-but-bounded inputs and external noises is proposed. The purpose of this deconvolution filter is to minimize the peak gain from the input signal and noise to the error by the viewpoint of the time domain. The solution consists of two steps. In the first step, the l₁ norm minimization problem is transferred to an equivalent A-norm minimization problem, and the minimum value of the peak gain is calculated. In the second step, based on the minimum peak gain, the l₁ optimal deconvolution filter is constructed by solving a set of constrained linear equations. Some techniques of inner-outer factorization, polynominal spectral factorization, linear programming, and some optimization theorems found in a book by Luenberger are applied to treat the l₁ optimal deconvolution filter design problem. Although the analysis of the algorithm seems complicated, the calculation of the proposed design algorithm for actual systems is simple. Finally, one numerical example is given to illustrate the proposed design approach. Several simulation results have confirmed that the proposed l₁ optimal deconvolution filter has more robustness than the l₂ optimal deconvolution filter under uncertain driving signals and noises     

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.