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Jones, Douglas L. Baraniuk, Richard Gordon 2014-12-16T22:22:55Z 2014-12-16T22:22:55Z 10000-01-01 1992 1992 Time-frequency representations are multidimensional transformations that indicate the joint time-frequency content of a signal. Representations such as the wavelet transform, the short-time Fourier transform, and the Wigner distribution have proven to be powerful tools for signal analysis and processing; however, current techniques are not without their drawbacks. This thesis presents two new approaches to time-frequency analysis that attempt to overcome two of the primary limitations inherent in current techniques. The lack of a single time-frequency representation that is "best" for all applications has resulted in a proliferation of representations, each corresponding to a different, fixed mapping from signals to the time-frequency plane. A major drawback of all fixed mappings is that, for each mapping, the resulting representation is satisfactory only for a limited class of signals. To counter this hindrance, we derive two new time frequency representations that adapt to each signal and thus perform well for a large class of signals. To find the "best" representation for a given signal, the design of each signal-dependent time-frequency representation is formulated as an optimization problem. The recent development of the wavelet transform has rekindled tremendous interest in proportional bandwidth, or "constant-Q," time-frequency analysis. In many applications, the time-scale analysis performed by the wavelet transform could be more appropriate than the constant-bandwidth analysis performed by representations such as the short-time Fourier transform, because it more closely matches the underlying physical mechanisms of some signals. However, the wavelet transform is ill-suited for the analysis of signals not exhibiting constant-Q structure. Using concepts from group representation theory, we propose the metaplectic transform, a transform that allows great freedom in the time-frequency resolution tradeoff and, hence, permits better matching of the transform to the signal characteristics. The metaplectic transform unites the conventional wavelet and short-time Fourier transforms under a common framework and provides a systematic method for designing new representations with resolution tradeoffs that are useful for certain types of signals. Using this framework, we construct two new classes of orthonormal bases for signals. A distinctive feature of these bases is that they are composed of linear-FM "chirp" functions. Made available in DSpace on 2014-12-16T22:22:55Z (GMT). No. of bitstreams: 1 9305460.pdf: 10034180 bytes, checksum: bfe9dde44a63eacc1f108ec9c2ad2b1a (MD5) Previous issue date: 1992 Embargo set by: Seth Robbins for item 72140 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 251 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992. http://hdl.handle.net/2142/71974 (UMI)AAI9305460 Mathematics Engineering, Electronics and Electrical Shear Madness: Signal-Dependent and Metaplectic Time-Frequency Representations text Electrical Engineering Electrical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.