{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/88162"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/88162","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On low-pass reconstruction and stochastic modeling of PWM signals","abstract":"Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis.","abstract_html":"Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis.","abstract_has_math":false,"creators":["Sevuktekin, Noyan Cem"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engineering","degree_department":null,"school":null,"contributors":["Singer, Andrew C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:49:44Z","date_published":"2015-09-29T20:49:44Z","updated_at":"2026-07-22T22:26:31Z","subjects":["pulse width modulation (PWM)","oversampling","low-pass reconstruction","natural sampling","uniform sampling","blurring effect"],"languages":["en"],"rights":["Copyright 2015 by Noyan Cem Sevuktekin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/88162","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Singer, Andrew C."]},{"key":"dc:creator","label":"Author","values":["Sevuktekin, Noyan Cem"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-29T20:49:44Z","2017-09-30T09:15:27Z","2015-08","2015-07-06","2015-8"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["pulse width modulation (PWM)","oversampling","low-pass reconstruction","natural sampling","uniform sampling","blurring effect"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 by Noyan Cem Sevuktekin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/88162"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Noyan Sevuktekin, accepted the attached license on 2015-07-06 at 11:30.","The student, Noyan Sevuktekin, submitted this Thesis for approval on 2015-07-06 at 11:47.","This Thesis was approved for publication on 2015-07-06 at 13:27.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8350 on 2015-09-29 at 14:59:10","Made available in DSpace on 2015-09-29T20:49:44Z (GMT). No. of bitstreams: 2 SEVUKTEKIN-THESIS-2015.pdf: 1499735 bytes, checksum: bfeab59b658e69ed7c4d8b4926ce8ecd (MD5) LICENSE.txt: 4213 bytes, checksum: e20b4cca60c28bef98ff84c0f8c941c8 (MD5) Previous issue date: 2015-07-06","Embargo set by: Seth Robbins for item 89442 Lift date: 2017-09-29T20:50:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 89442 on 2017-09-30T09:15:27Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On low-pass reconstruction and stochastic modeling of PWM signals"]}]}],"canonical_facts":{"dc:contributor":["Singer, Andrew C."],"dc:creator":["Sevuktekin, Noyan Cem"],"dc:date":["2015-09-29T20:49:44Z","2017-09-30T09:15:27Z","2015-08","2015-07-06","2015-8"],"dc:description":["Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Noyan Sevuktekin, accepted the attached license on 2015-07-06 at 11:30.","The student, Noyan Sevuktekin, submitted this Thesis for approval on 2015-07-06 at 11:47.","This Thesis was approved for publication on 2015-07-06 at 13:27.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8350 on 2015-09-29 at 14:59:10","Made available in DSpace on 2015-09-29T20:49:44Z (GMT). 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