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.
