Joint Density-Based Methods of Applied Nonstationary Signal Processing

虽然傅立叶变换是信号处理和线性时不变（LTI）系统分析中不可或缺的工具，也是电气工程教育的主要内容，但许多自然和人为过程不是时不变的，而是表现出随时间变化的频率（例如，FM通信系统、多普勒效应、语音和其他生物医学信号）。 传统的短时间，或“准静态”，扩展的LTI概念研究这样的过程往往是不够的，例如，取决于所选择的短时间分析间隔长度，可以获得显着不同的结果为同一过程，特别是当信号包含瞬态和谐波。 因此，在工程实践和教学中，都需要开发用于时变（或非平稳）信号处理的新方法。 本研究涉及非平稳信号处理的一般方法的开发和应用，克服了基于LTI概念扩展到时变情况的方法的局限性。 本研究的主要目标是：（1）开发新的联合密度为基础的非平稳信号处理方法（例如，scale）;（2）将这些新方法应用于生物医学信号分析和机器健康监测（属于生物技术和制造联邦战略领域）中具有挑战性的实际问题;（3）通过新的教学实验室课程和大学本科生和研究生的研究机会，为基于新方法的非平稳信号处理开发一个通用教育框架。

While the Fourier transform is an indispensable tool in signal processing and linear time-invariant (LTI) systems analysis, as well as a staple of the electrical engineering education, many natural and man-made processes are not time-invariant but rather exhibit frequencies that change over time (e.g., FM communication systems, the Doppler effect, speech and other biomedical signals). The conventional short-time, or "quasi-stationary," extensions of LTI concepts for studying such processes is often inadequate; for example, depending upon the short-time analysis interval length selected, dramatically different results can be obtained for the same process, particularly when the signal contains both transients and harmonics. Accordingly, there is a need, both in engineering practice and pedagogy, for the development of new methods for time- varying (or nonstationary) signal processing. This research involves the development and application of a general method of nonstationary signal processing that surmounts the limitations of methods based on the extension of LTI concepts to time-varying situations. The principle objectives of this research are to: (1) develop new joint density-based methods for nonstationary signal processing (e.g., scale); (2) apply these new methods to challenging, practical problems in biomedical signal analysis and machine health monitoring (which fall under the biotechnology and manufacturing Federal Strategic Areas); and, (3) develop a general educational framework for nonstationary signal processing based on the new methods, via new instructional laboratory courses and research opportunities for college undergraduate and graduate students.