【作者】 苏飞；

【导师】 王兆华；

【作者基本信息】 天津大学 ， 信号与信息处理， 2003， 博士

【摘要】 本论文探讨变换域带窗重叠数字滤波器以及它在自适应信号处理、二维滤波模板设计、谱分析以及图像的多分辩率分析等方面的应用。首先，提出前后加窗的N阶频域重叠数字滤波器—全相位数字滤波器(简记为APF)。它的输出等于与某时刻输入相关的N段信号作为系统输入时所产生的N个输出和的平均。在此基础上，提出DCT域、DWA域APF的概念，理论推导得出相应的反变换域对应的FIR模型，并提出无窗、单窗和双窗系统的概念。全相位数字滤波器成功解决了分段处理所带来的截断效应，滤波效果优于非重叠处理。其次，经过对APF的幅频和相频特性的分析，并给出了APF系统具有严格线性相位、满足频域抽样定理的条件。为提高系统的功能，提出“基于LMS准则”和“基于矩形二叉分解”的窗函数设计算法，其中二叉分解算法将系统窗看作由二叉树中左右分支的低阶矩形窗卷积形成，并依据回归定义形成多级分解。实验表明，由这两种算法得到的窗很好地减少了滤波器在通带和阻带中的波纹并可获得大的阻带衰减。第三，通过对APF滤波实质的分析，提出加权重叠(WO)算法。运用此算法于自适应信号处理中，提出了基于LMS准则的时域WO-LMS算法和变换域WO-TLMS算法。自适应辨识实验结果表明，此算法具有收敛速度快和稳态误差小的双重优点；实验中，在谱分析、模板设计和多分辨分析中运用WO算法，都取得好的效果。最后，利用MATLAM软件中的SIMULINK模块，仿真实现并验证了APF的滤波功能和优点。更多还原

【Abstract】 This dissertation deals mainly with windowed overlapping digital filter in transform domain, including its application in adaptive signal processing、design of 2-dimensional filtering template、spectrum analysis and multiresolution analysis of image, etc. First, the paper presents a novel N-order overlapping digital filter with front and back windows in frequency domain—all phase digital filter(APF), which output equals to the mean of sum of outputs from the system with N fragmentary inputs relevant to the signal at some time. Based on this module, some other notions as APF in DCT domain、DWA and DST domain are advocated as well. And the corresponding FIR modules are theoretically deduced out respectively, as well as proposing no-window、single-window and dual-window system. It can be verified by experimental results that all phase digital filter successfully eliminates the distortion resulting from truncating, with much better effect than fragmentary processing.Secondly, the conditions for strict linear phase、sampling theorem in frequency domain of AOF system are presented in detail through analysis of its amplitude and phase characteristics to frequency. In order to promote the performance of AOF system, two algorithms on how to efficiently design the window, one of which is based on LMS principle and the other is bifurcating of rectangle window which treats the system window as being formed from the convolution of two lower-ordered rectangle window on the left and right branch of the dichotomic tree and therewith forms multilevel decomposition via recursion, are put forward. Experimental results have shown AOF system with such window function not only decreases the ripples over both pass and stop bands, but also can achieve far lower stopband attenuation than average.Thirdly, by the analysis of essence of filtering of AOF, a new algorithm of windowed overlapping(WO) is advanced. By exploiting WO in adaptive signal processing, two new algorithms in both time domain known as WO-LMS and transform domain known as WO-TLMS are developed. Results of experiment about adaptive recognition indicates that this algorithm bears such two merits as faster convergence speed and lower steady error than conventional LMS. Applying WO-LMS algorithm in spectrum analysis、module designing and multiresolution analysis respectively gives birth to favorable results.Finally, by making use of the SIMULINK module in software MATLAB, functions and fine performance of AOF are validated in the simulation.更多还原