{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/10092"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/10092","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Wavelet Analysis and its Application to Modulation Characterization","abstract":"Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. The results show that selective forcing affects the time-variations of the phase relation. In a third application, the magnitude and phase of the wavelet coefficients are used to decompose propagating waves measured at a single location.","abstract_html":"Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. The results show that selective forcing affects the time-variations of the phase relation. In a third application, the magnitude and phase of the wavelet coefficients are used to decompose propagating waves measured at a single location.","abstract_has_math":false,"creators":["Lusk, Craig Perry"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Hajj, Muhammad R."],"committee_members":["Hendricks, Scott L.","Ragab, Saad A."],"year":2004,"date_issued":"2004-06-05","date_published":"2004-06-05","updated_at":"2026-07-22T22:19:15Z","subjects":["Hydrodynamic Stability","Mixing Layers","Modulation","Wavelets","Waves"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-052699-144606"],"render_values":[{"text":"etd-052699-144606","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/10092","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Hajj, Muhammad R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hendricks, Scott L.","Ragab, Saad A."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Lusk, Craig Perry"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-08-06T16:06:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-08-06T16:06:15Z","2000-05-26"]},{"key":"dc:date.issued","label":"Date","values":["2004-06-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hydrodynamic Stability","Mixing Layers","Modulation","Wavelets","Waves"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-052699-144606"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/10092"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. The results show that selective forcing affects the time-variations of the phase relation. In a third application, the magnitude and phase of the wavelet coefficients are used to decompose propagating waves measured at a single location."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Wavelet Analysis and its Application to Modulation Characterization"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hajj, Muhammad R."],"dc:contributor.committeemember":["Hendricks, Scott L.","Ragab, Saad A."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Lusk, Craig Perry"],"dc:date.accessioned":["2011-08-06T16:06:15Z"],"dc:date.available":["2011-08-06T16:06:15Z","2000-05-26"],"dc:date.issued":["2004-06-05"],"dc:description.abstract":["Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. 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