Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.
","abstract_html":"<p>Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.</p>","abstract_has_math":false,"creators":["Chisholm, David"],"institution":null,"degree_name":"Master of Science (M.S.)","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Izidor Gertner","Douglas Troeger"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T01:57:08Z","subjects":["Gabor Analysis","Time frequency","Wilson basis","Computer Sciences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/cc_etds_theses/550","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Izidor Gertner","Douglas Troeger"]},{"key":"dc:creator","label":"Author","values":["Chisholm, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-11T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Gabor Analysis","Time frequency","Wilson basis","Computer Sciences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/cc_etds_theses/550"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.
"]},{"key":"dc:title","label":"Title","values":["DISCRETE TRANSFORMS WITH GOOD TIME-FREQUENCY AND SPATIAL-FREQUENCY LOCALIZATION"]}]}],"canonical_facts":{"dc:contributor":["Izidor Gertner","Douglas Troeger"],"dc:creator":["Chisholm, David"],"dc:date.available":["2016-02-11T08:00:00Z"],"dc:description.abstract":["Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.
"],"dc:identifier":["https://academicworks.cuny.edu/cc_etds_theses/550"],"dc:subject":["Gabor Analysis","Time frequency","Wilson basis","Computer Sciences"],"dc:title":["DISCRETE TRANSFORMS WITH GOOD TIME-FREQUENCY AND SPATIAL-FREQUENCY LOCALIZATION"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (M.S.)"]},"updated_at":"2026-07-24T01:57:08Z"}