Theory and Application of Dispersive Multirate Filterbacks and Wavelets

这个教师早期职业发展建议的研究部分旨在开发一个大的，重要的，从根本上讲是新的一类多速率滤波器组，系统和小波。 传统的发展，这一主题在信号处理社区的强烈动机的应用程序涉及信号分析。 与此形成强烈对比的是，本提案中的研究是由涉及信号合成的一些重要的当代应用所激发的。 特别是，多速率滤波器组理论，小波理论有一个潜在的重要的和很大程度上未开发的作用，在各种各样的宽带通信和删除传感应用的波形合成。 在这些应用中，根本上不同类型的设计标准和约束在开发合适的多速率结构中发挥作用。 其中最重要的区别是，虽然对于大多数应用程序，涉及信号分析强本地化的时间和频率是强调，这将是这项工作的重点应用的种类将需要滤波器组和小波的能量是广泛分散在时间和频率。 我们建议探讨几类正交和双正交色散，“伪随机”滤波器组和小波基。 几个具体的应用领域将在拟议的研究下进行。 其中一个重点将是数字无线通信。 在这里，色散滤波器组和小波有望导致新的码分复用系统，更有效地对抗衰落，干扰和其他形式的多址干扰。 此外，我们计划实施新的无线调制解调器，我们开发的基于DSP的，实时900兆赫室内无线系统测试平台最近开发的主要研究者作为他的无线通信实验室的一部分。 该提案的教育部分包括本科和研究生两级的重要课程开发，以及对研究生指导的大力投资。 其中一项教学举措涉及最近推出的一个统一的新本科科目的发展。 本课程首次向本科生介绍通信，控制和信号处理的基础知识，并建立在基本信号，系统和概率的基础上。 第二个主要的教学计划涉及麻省理工学院随机过程，检测和估计的基础研究生课程的重新设计。 在这个主题中，目标是重新开发教学大纲，课程笔记，Matlab计算机练习和家庭作业问题，强调现代，统一的观点，随机和确定性信号和相关的信号处理算法。 这些课程的变化也将允许一些先进的主题，包括多尺度和非线性信号处理，被纳入。 教育计划的最后一个组成部分是继续积极指导不同群体的研究生，培养他们的智力，专业和个人成长。 当然，最终，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.