Joint Density-Based Methods of Applied Nonstationary Signal Processing

虽然傅里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性的，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)。用传统的LTI概念的短时或准平稳扩展来研究这类过程往往是不够的；例如，根据所选择的短时分析间隔长度，对于相同的过程，可能会得到截然不同的结果，特别是当信号同时包含瞬变和谐波时。因此，在工程实践和教学中，都需要开发处理时变(或非平稳)信号的新方法。这项研究涉及开发和应用一种通用的非平稳信号处理方法，该方法克服了基于LTI概念扩展到时变情况的方法的局限性。这项研究的主要目标是：(1)开发新的基于联合密度的非平稳信号处理方法(例如，尺度)；(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业联邦战略领域)中具有挑战性的实际问题；以及(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，基于新方法开发非平稳信号处理的一般教育框架。

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.