Theory and Design of Filter Banks and Wavelets with Applications in Signal Conversion, Adaptation, Detection and Classification

本项目主要研究完全重构(PR)/NCAR完全重构(NPR)滤波器组的原理、结构和设计方法，以及它们在信号转换、检测和自适应中的应用。在音频压缩算法、高带宽高分辨率A/D转换器、宽带信号检测系统和自适应滤波算法等应用中，需要具有高衰减特性的高性能滤波器组。由于这些参数与目标函数之间的非线性关系，使得这些滤波器组的设计非常困难。将研究新的结构和设计方法。他们将开辟新的滤波器组类别，其中一些在该项目中得到了解决。它们是双正交余弦调制滤波器组、无限冲激响应余弦调制滤波器组和非均匀滤波器组。这些滤波器组将用于高性能A/D转换器、无损评估、回声消除和自适应噪声消除系统等多个应用中。教学部分包括编写一本关于滤波器组小波的理论和设计方法的本科教科书，建立一个存储滤波器组设计程序和系数的网站，并开发一门关于时频和时间尺度分析的新课程。

The proposed project is focused on the theory, structure and design methods for the perfect-reconstruction (PR) /ncar-perfect- reconstruction (NPR) filter banks and their applications in signal conversion, detection and adaptation. High performance filter banks with high attenuation are needed in many applications such as audio compression algorithms, high-bandwith high-resolution A/D converters, wideband signal detection systems and adaptive filtering algorithms. The design of these filter banks are very difficult because of the nonlinear relations between the parameters and the objective function. New structures and design methods will be investigated. They will open up new classes of filter banks, some of which are addressed in the project. They are the biorthogonal cosine-modulated filter bank, the infinite-impulse- response (IIR) cosine-modulated filter bank, and the nonuniform filter bank. These filter banks will be used in several applications such as high-performance A/D converter, nondestructive evaluation, echo cancellation and adaptive noise cancellation systems. The education part consists of writing an undergraduate textbook on the theory and design methods of filter bank wavelets, establishing an internet site for the storage of design programs and coefficients of filter banks and developing a new course on time- frequency and time-scale analysis.