CAREER: Systems for Linear and Nonlinear Signal Analysis - Design via Groebner Bases

CCR-9875452 Selesnick Polytechnic University滤波和变换理论是压缩、传输和分析来自生物医学、地质或娱乐来源的音频、图像或视频格式信号的基础。由于许多自然信号的非线性模型比线性模型更准确地建模，因此追求非线性变换的设计，实现和评估尤为重要。本研究通过将代数几何中强大的数学工具应用于线性和非线性信号分析系统的设计，推进了最先进的多分辨率分析工具。Groebner基的使用从根本上提高了人们构建离散时间系统的能力，即使相应的设计方程是非线性的。这项研究将导致更深入地了解如何成功地应用Groebner基地在实践中，他们的局限性是什么，调查员还将组织一个互联网网站，“信号处理练习和实验室银行”，致力于信号处理教育。该网站将不断收集教育工作者和研究人员提供的创新练习、项目和演示，说明基本理论及其在现实世界信号中的应用，并可以更新以反映信号处理技术的进展。它将促进信号处理研究和教育的整合，并将同样有助于SP课程的现代化，通过为教育工作者提供一系列介绍性练习，说明最近和正在进行的研究主题。通过汇集现有的资源，并提供一个点，为未来的创新练习和实验室的传播，该网站将加强美国国家科学基金会的现有投资在信号处理教育和研究。

CCR-9875452SelesnickPolytechnic UniversityThe theory of filtering and transforms is fundamental for the compression, transmission, and analysis of signals from biomedical, geological, or entertainment sources, in audio, image, or video format. Because many natural signals are modeled more accurately by nonlinear models than by linear models, it is especially important to pursue the design, implementation and evaluation of nonlinear transforms. This researchadvances the state-of-the-art multiresolution analysis tools by bringing powerful mathematical tools from algebraic geometry to bear upon the design of systems for linear and nonlinear signal analysis. The use of Groebner bases fundamentally improves one's ability to construct discrete-time systems, even when the corresponding design equations are nonlinear. This research will lead to a deeper understanding of how to successfully apply Groebner bases in practice, and what their limitations are.The investigator will also organize an Internet website, `A Signal Processing Exercise and Lab Bank', devoted to signal processing education. The website will be an evolving collection of innovative exercises, projects and demos contributed by educators and researchers, that illustrate both basic theory and its application to real-world signals, and which can be updated to reflect the progress in signal processing techniques. It will facilitate the integration of signal processing research and education, and will likewise help in modernizing SP curriculums, by giving educators access to a collection of introductory exercises illustrating recent and ongoing research topics. By drawing together existing resources, and by providing a point for the dissemination of future innovative exercises and labs, the website will enhance the NSF's existing investment in signal processing education and research.