CAREER: Wavelet-Based Nonlinear Digital Signal Processing

数字计算能力的快速增长，以及通信、生物医学、制造、地震、雷达和各种商业和科学兴趣的其他信号对快速、可靠的计算机处理技术的需求，推动了数字信号处理（DSP）的应用。尽管传统的DSP技术取得了巨大的成功，但由于在这些应用中经常遇到非线性和非高斯噪声，许多现实世界的问题仍然没有得到解决。解决这些更复杂的问题需要开发新的、更灵活的非线性DSP理论和工具。这个项目的目标是发展这些新的工具和理论，并将它们直接转化为实践和工程课堂。目前正在研究一种基于小波变换的非线性DSP框架。小波变换的特性，如时频定位和信号压缩，正被用来开发复杂而又易于处理的非线性处理技术。工作的关键要素包括发展统计重采样方法和非线性DSP的数据自适应小波分析。正在研究将新框架应用于成像和通信领域的跨学科问题。首席研究员同时开发工程教育的创新方法，包括基于互联网的教程和新研究的文档，跨学科的学生设计项目，以及课程评估工具。

The application of Digital Signal Processing (DSP) has been driven by the rapid growth of digital computing power and the need for fast, reliable computer processing techniques for communication, biomedical, manufacturing, seismic, radar, and a wide variety of other signals for commercial and scientific interest. Despite the great success of traditional DSP techniques, many real- world problems remain unsolved due to the nonlinearities and non-Gaussian noises often encountered in these applications. Solving these more complex problems requires the development of new, more flexible, nonlinear DSP theory and tools. The objectives of this project are to develop these new tools and theory, and to transfer them directly into practice and into the engineering classroom. A new framework for nonlinear DSP based on the wavelet transform is currently under study. The desirable properties of the wavelet transform, such as time- frequency localization and signal compression, are being exploited to develop sophisticated, yet tractable, nonlinear processing techniques. Key elements of the work include the development of statistical re-sampling methods and data- adaptive wavelet analyses for nonlinear DSP. Applications of the new framework to cross-disciplinary problems in imaging and communications are being investigated. The principal investigator is concurrently developing innovative approaches to engineering education including Internet-based tutorials and documentation of new research, cross-disciplinary student design projects, and tools for curriculum assessment.