Signal Adaptive Frame Theory

Adaptive frequency band (AFB) and ultra-wide-band (UWB) systems require either rapidly changing or very high sampling rates. Conventional analog-to-digital devices have non-adaptive and limited dynamic range. We investigate AFB and UWB signal processing via a basis projection method.

The method first windows the signal and then decomposes the signal into a basis via a continuous-time inner product operation, computing the basis coefficients in parallel. The windowing systems are key, and we develop systems that have variable partitioning length, variable roll-off and variable smoothness. These include smooth bounded adaptive partitions of unity (BAPU systems) created using B-splines, systems developed to preserve orthogonality of any orthonormal systems between adjacent blocks, and almost orthogonal windowing systems that are more computable/constructible than the orthogonality preserving systems. We construct the basis projection method for all three types of windows, analyze various methods for signal segmentation and create systems designed for binary signals. The projection method is, in effect, an adaptive Gabor system for signal analysis. The natural language to express this structure is frame theory. We finish our talk by developing projection as signal adaptive frame theory.

Speaker Bio: Professor Stephen D. Casey is founding member of the Editorial Board for Sampling Theory in Signal and Image Processing. His research is in complex and harmonic analysis with applications to signal and image processing. He has been a Visiting Research Professor at the Institute for Systems Research (ISR) at the University of Maryland, and was a Visiting Research Professor at the Norbert Wiener Center for Harmonic Analysis (NWC) at the University of Maryland. He was recently invited to be an Associate Editor of The Journal of Signal and Image Processing. He has published nearly fifty articles, and is completing work on two invited books. He has given nearly one hundred talks, lecturing at various universities in Europe, Asia and North America. His research has been funded by 15 research grants and 4 contracts, including grants from the National Science Foundation, the Office of Naval Research, the Army Research Office and the Air Force Office of Scientific Research. He was awarded two provisional patents in 2011 for his work in signal adaptive processing.

Presentation Slides: PDF

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