滤波器组格型结构自由参数的初始化研究

The design of filter bank can be efficiently carried out via lattice structure. Such obtained filter banks include free parameters, which can be optimized to produce more practical filter banks. Unfortunately, the optimization is highly nonlinear thus very sensitive to the initial values of the free parameters. Therefore, the initialization of the free parameters is important before starting the optimization, and such issue will be addressed in this proposal. The idea of the proposal is to initialize the free parameter values in complicated cases to be those in simple cases where practical filter banks can be easily obtained. Three ways will be applied for this idea. They are initializing the high-order case to be the low-order case, initializing the arbitrary-length case to be the constrained-length case, as well as initializing the oversampled case to be the critically-sampled case. In the three ways, the simple cases are low-order, constrained-length, and critically-sampled cases respectively, and the complicated cases are high-order, arbitrary-length, and oversampled cases respectively. The obtained theory based upon the three ways about the initialization of the free parameters in lattice structure of filter banks will consider particularly two important properties, i.e., linear phase and perfect reconstruction; and the related results will be applicable to various filter banks, including special ones that are constrained-length and/or critically-sampled, as well as general ones that are arbitrary-length and/or oversampled.

格型结构在滤波器组的设计上非常有效。它生成的滤波器组包含自由参数，自由参数的值通过优化算法调整后，对应滤波器组的工程实用性更佳。然而此中涉及的优化是高度非线性的，以致对自由参数的初值非常敏感。因此滤波器组格型结构自由参数的初始化是一个极为重要的科学问题，而这正是本项目的研究主题。本项目的思想是- - 将待优化的复杂情形的自由参数值初始化为易获得实用滤波器组的简单情形的自由参数值。将采用的思路有三条，分别是低阶情形对高阶情形的初始化，约束长度情形对任意长度情形的初始化，以及严格采样情形对过采样情形的初始化；其中简单情形分别为低阶、约束长度与严格采样情形，而复杂情形分别为高阶、任意长度与过采样情形。借由此三条思路建立的滤波器组格型结构自由参数的初始化理论，将特别考虑线性相位与完全重构两种重要性质；所得结果既适用于约束长度与（或）严格采样的特殊滤波器组，又可用于任意长度与（或）过采样的一般滤波器组。

格型结构设计的滤波器组包含自由参数，相关优化高度非线性因而对自由参数初值较为敏感。本项目主要研究滤波器组格型结构自由参数的初始化问题，同时也关注与此紧密相关的滤波器组格型结构设计问题。在自由参数初始化上，项目组提出简单情形初始化复杂情形的思路，实现了低阶情形对高阶情形的初始化，以及约束长度情形对任意长度情形的初始化；对应初始化方法可确保之后优化所生成滤波器组的实用性，相应结果分两次发表在国际权威期刊《Signal Processing》。在滤波器组格型结构设计上，项目组构造了多维情形与过采样情形的满足线性相位与完全重构性质的滤波器组，此外也构造了满足正则性的滤波器组，这些构造结果发表在《IEEE Transactions on Image Processing》、《IEEE Signal Processing Letters》等国际权威期刊。项目组共完成SCI期刊论文5篇，其中包含IEEE期刊论文2篇。