Resolution, Coherence and Distance between Density Functions

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Intellectual merit:The main thrust of the proposed research is to develop tools and quantitative measures for robust high resolution signal analysis. A range of tools is envisaged and outlined --from versions of a multivariable-periodogram applied to generalized statistics, to mathematical solutions of spectral inverse problems. Distance metrics for assessing spectral uncertainty are suggested which quantify differences in predictive qualities between two time-series. These metrics are sought to quantify the quality of estimation and to provide a means to tune estimation algorithms. Emphasis is placed on the analysis of vectorial processes in spacio-temporal domains. A concept of causal coherence is being proposed for use in control applications, as exemplified by problems of noise suppression and vibration isolation.Broader impact:Signal analysis is a critical technology behind a wide range of applications. Recent collaborative work of the principal investigator on non-invasive temperature sensing via ultrasound (for e.g., computer guided tumor ablation and therapy) and on vibration isolation experiments utilizing distributed sensor arrays, underscore the need for the proposed research and its potential to enhance pertinent technological advances. The research may impact an even greater range of technologies involving distributed sensor arrays, identification, modeling and data mining. An experimental set up to demonstrate relevant concepts of estimation and control for educational purposes will be developed and, in coordination with the Science Museum of Minnesota, it will be planned as an exhibit in the physical sciences and technology section of the museum