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Title:  Shear Madness: SignalDependent and Metaplectic TimeFrequency Representations 
Author(s):  Baraniuk, Richard Gordon 
Doctoral Committee Chair(s):  Jones, Douglas L. 
Department / Program:  Electrical Engineering 
Discipline:  Electrical Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics
Engineering, Electronics and Electrical 
Abstract:  Timefrequency representations are multidimensional transformations that indicate the joint timefrequency content of a signal. Representations such as the wavelet transform, the shorttime 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 timefrequency analysis that attempt to overcome two of the primary limitations inherent in current techniques. The lack of a single timefrequency 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 timefrequency 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 signaldependent timefrequency representation is formulated as an optimization problem. The recent development of the wavelet transform has rekindled tremendous interest in proportional bandwidth, or "constantQ," timefrequency analysis. In many applications, the timescale analysis performed by the wavelet transform could be more appropriate than the constantbandwidth analysis performed by representations such as the shorttime Fourier transform, because it more closely matches the underlying physical mechanisms of some signals. However, the wavelet transform is illsuited for the analysis of signals not exhibiting constantQ structure. Using concepts from group representation theory, we propose the metaplectic transform, a transform that allows great freedom in the timefrequency resolution tradeoff and, hence, permits better matching of the transform to the signal characteristics. The metaplectic transform unites the conventional wavelet and shorttime 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 linearFM "chirp" functions. 
Issue Date:  1992 
Type:  Text 
Description:  251 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1992. 
URI:  http://hdl.handle.net/2142/71974 
Other Identifier(s):  (UMI)AAI9305460 
Date Available in IDEALS:  20141216 
Date Deposited:  1992 
This item appears in the following Collection(s)

Dissertations and Theses  Electrical and Computer Engineering
Dissertations and Theses in Electrical and Computer Engineering 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois