{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71974"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71974","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Shear Madness: Signal-Dependent and Metaplectic Time-Frequency Representations","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Baraniuk, Richard Gordon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Jones, Douglas L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T22:22:55Z","date_published":"2014-12-16T22:22:55Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Mathematics","Engineering, Electronics and Electrical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9305460"],"render_values":[{"text":"(UMI)AAI9305460","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71974","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jones, Douglas L."]},{"key":"dc:creator","label":"Author","values":["Baraniuk, Richard Gordon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T22:22:55Z","10000-01-01","1992"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Engineering, Electronics and Electrical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71974","(UMI)AAI9305460"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Shear Madness: Signal-Dependent and Metaplectic Time-Frequency Representations"]}]}],"canonical_facts":{"dc:contributor":["Jones, Douglas L."],"dc:creator":["Baraniuk, Richard Gordon"],"dc:date":["2014-12-16T22:22:55Z","10000-01-01","1992"],"dc:description":["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."],"dc:identifier":["http://hdl.handle.net/2142/71974","(UMI)AAI9305460"],"dc:subject":["Mathematics","Engineering, Electronics and Electrical"],"dc:title":["Shear Madness: Signal-Dependent and Metaplectic Time-Frequency Representations"],"dc:type":["text"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:05Z"}