{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1647"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1647","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Optimal and Permissible Sampling Rates for First-Order Sampling of Two-Band Signals","abstract":"Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals.","abstract_html":"Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals.","abstract_has_math":false,"creators":["Linder, Daniel Frederick"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["David Stone","Goran Lesaja"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-05-01T07:00:00Z","date_published":"2008-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Nyquist rate","Digital signal processing","Sampling","Passband","Signal","Signal processing"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/647","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["David Stone","Goran Lesaja"]},{"key":"dc:creator","label":"Author","values":["Linder, Daniel Frederick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Nyquist rate","Digital signal processing","Sampling","Passband","Signal","Signal processing"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/647"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals."]},{"key":"dc:title","label":"Title","values":["Optimal and Permissible Sampling Rates for First-Order Sampling of Two-Band Signals"]}]}],"canonical_facts":{"dc:contributor":["David Stone","Goran Lesaja"],"dc:creator":["Linder, Daniel Frederick"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/647"],"dc:subject":["ETD","Nyquist rate","Digital signal processing","Sampling","Passband","Signal","Signal processing"],"dc:title":["Optimal and Permissible Sampling Rates for First-Order Sampling of Two-Band Signals"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}