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New Techniques in Time-Frequency Analysis: Adaptive Band, Ultra-Wide Band and Multi-Rate Signal Processing

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Technical Report,01 Sep 2012,31 Aug 2015

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American University Washington United States

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The project led to the development of new techniques and theories in the analysis of signals. These techniques and theories were extensions of known techniques -- sampling, Fourier, Gabor and wavelet analysis, and new approaches to analysis -- using combinations of analysis, geometry, group theory, and number theory. Every target item in the original statement of objectives was achieved, and several new areas of research were open up. There were four main areas of study i Techniques were developed to deal with classes of signals for which the known techniques have limitations, e.g., adaptive frequency band AFB and ultra-wide band UWB signals ii Techniques for multi-rate sub-Nyquist sampling were developed. This then allows for processing of wider bandwidth signals at smaller bandwidth rates iii We also developed a program of study connecting sampling theory with the geometry of the signal and its domain. In particular, we established Nyquist tiles and sampling groups in Euclidean geometry, and discussed the extension of these concepts to hyperbolic and spherical geometry and general orientable surfaces iv We have developed a collection of algorithms that analyze periodic point processes, including analysis of generators and deinterleaving.

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