Theory of Time-Frequency and Time-Scale Analysis: Almost all physical signals come from systems that are time-varying. Our theory drops all the typical assumptions of stationary increments in time (and space) and is able to directly resolve spectral detail while preserving time dynamics. This theory has been extended to develop optimal time-frequency smoothers for classification and detection applications. Current work is directed toward providing a theoretical foundation for spectral analysis and transformations of the dynamics of time-varying systems. This theory has been applied to sonar, radar, machine and manufacturing monitoring, and speech and music signal analysis. Biomimetic Acoustic Analysis: An interdisciplinary team of researchers from the University of Maryland, Boston University and the University of Washington are providing new principals for acoustic analysis. Prof. Atlas has provided this team with a new framework for understanding how auditory systems represent signals which are time-varying. This new approach, called "autoambiguity analysis," has improved the performance of systems used in manufacturing, machine monitoring, and sonar applications.