Theory and Application of Dispersive Multirate Filterbacks and Wavelets

这项教师早期职业发展建议的研究部分旨在开发一大类重要的、从根本上说是新的多速率滤波器组、系统和小波。这一主题在信号处理领域的传统发展一直受到涉及信号分析的应用程序的强烈推动。与此形成鲜明对比的是，这一提议的研究是由涉及信号合成的一些重要的当代应用所推动的。特别是，多速率滤波器组理论、小波理论在各种宽带通信和去除侦听应用的波形合成中具有潜在的重要且在很大程度上未被探索的作用。在这些应用中，根本不同类型的设计标准和约束在开发合适的多速率结构方面发挥了作用。最重要的区别之一是，尽管对于大多数涉及信号分析的应用来说，强调了时间和频率上的强局部化，但将成为本工作重点的应用类型将需要能量在时间和频率上广泛分散的滤波器组和小波。我们建议探索几类正交和双正交色散、“伪随机”滤波器组和小波基。拟议的研究将涉及几个具体的应用领域。其中一个重点将是数字无线通信。在这里，分散的滤波器组和小波有望导致新的码分多工系统，从而更有效地对抗衰落、干扰和其他形式的多址干扰。此外，我们计划在首席研究人员最近开发的基于DSP的实时900 Mz室内无线系统测试床上实现我们开发的新无线调制解调器，作为其无线通信实验室的一部分。该提案的教育部分包括在本科生和研究生阶段大力开发课程，并大力投资指导研究生。其中一项教学举措涉及开发一门最近引入的统一的本科新科目。本课程第一次向本科生介绍通信、控制和信号处理的基本原理，从一个共同的角度，建立在基本信号、系统和概率的基础上。第二个主要的教学举措涉及麻省理工学院关于随机过程、检测和估计的基础研究生课程的重新设计。在这门课程中，目标是重新制定教学大纲、课程笔记、MatLab计算机练习和家庭作业问题，强调对随机和确定性信号及其相关信号处理算法的现代统一观点。这些课程的改变还将允许包括多尺度和非线性信号处理在内的许多高级主题被纳入。教育计划的最后一个组成部分包括继续积极指导不同的研究生群体，并培养他们的智力、专业和个人成长。当然，归根结底，这种互动是学术生涯中最令人满意和最重要的方面之一。

The research component of this faculty early career development proposal is aimed at developing a large, important, and fundamentally new class of multirate filter banks, systems and wavelets. Traditional developments of this topic within the signal processing community have been strongly motivated by applications involving signal analysis. In strong contrast, the research in this proposal is motivated by some important contemporary applications involving signal synthesis. In particular, multirate filterbank theory, wavelet theory have a potentially important and largely unexplored role to play in the synthesis of waveforms for a wide variety of broadband communications and remove sensing applications. In these applications, fundamentally different types of design criteria and constraints come into play in developing suitable multirate structures. Foremost among the important differences is that while for most applications involving signal analysis strong localization in time and frequency is emphasized, the kinds of applications that will be the focus of this work will require filterbanks and wavelets whose energy is widely dispersed in both time and frequency. We propose to explore several classes of orthogonal and biorthogonal dispersive, "pseudorandom" filterbanks and wavelet bases. Several specific application areas are to be pursued under the proposed research. One that will be emphasized will be digital wireless communications. Here dispersive filterbanks and wavelets are expected to lead to new code-division multiplexing systems that more efficiently combat fading, jamming, and other forms of multiple-access interference. Furthermore, we plan to implement the new wireless modems we develop in a DSP-based, real-time 900 Mz indoor wireless system testbed recently developed by the principal investigator as part of his wireless communications laboratory. The educational component of the proposal encompasses significant curriculum development at b oth the undergraduate and graduate levels, and a strong investment in the mentoring of graduate students. One teaching initiative involves the development of a recently introduced unified new undergraduate subject. This subject introduces undergraduate students, for the first time, to the fundamentals of communications, control and signal processing from a common perspective and which builds on a foundation of basic signals, systems, and probability. The second major teaching initiative involves the re-engineering of the fundamental graduate subject on stochastic processes, detection and estimation at MIT. In this subject, the object is to redevelop a syllabus, course notes, Matlab computer exercises, and homework problems that emphasize modern, unified perspective to random and deterministic signals and the associated signal processing algorithms. These curricular changes will also allow a number of advanced topics, including multiscale and nonlinear signal processing, to be incorporated. A final component of the education plan involves continued active mentoring of a diverse group of graduate students and nurturing their intellectual, professional, and personal growth. Ultimately, of course, this interaction is one of the most gratifying and important aspects of a academic career.