{"id":"https://openalex.org/W3198386996","doi":"https://doi.org/10.1109/msp.2021.3090681","title":"Tracking and Estimation of Frequency, Amplitude, and Form Factor of a Harmonic Time Series [Lecture Notes]","display_name":"Tracking and Estimation of Frequency, Amplitude, and Form Factor of a Harmonic Time Series [Lecture Notes]","publication_year":2021,"publication_date":"2021-08-27","ids":{"openalex":"https://openalex.org/W3198386996","doi":"https://doi.org/10.1109/msp.2021.3090681","mag":"3198386996"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2021.3090681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2021.3090681","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040056296","display_name":"Ronald M. Aarts","orcid":"https://orcid.org/0000-0003-3194-0700"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Ronald M. Aarts","raw_affiliation_strings":["Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-3194-0700","affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040056296"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.08378663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"38","issue":"5","first_page":"86","last_page":"91"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11196","display_name":"Non-Invasive Vital Sign Monitoring","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11196","display_name":"Non-Invasive Vital Sign Monitoring","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11700","display_name":"Hemodynamic Monitoring and Therapy","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2746","display_name":"Surgery"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10745","display_name":"Heart Rate Variability and Autonomic Control","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/harmonics","display_name":"Harmonics","score":0.6215720772743225},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.5670127272605896},{"id":"https://openalex.org/keywords/crest-factor","display_name":"Crest factor","score":0.5218122005462646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5008382797241211},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.48216646909713745},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.47155046463012695},{"id":"https://openalex.org/keywords/sine-wave","display_name":"Sine wave","score":0.46467310190200806},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.462862104177475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46126702427864075},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.45286130905151367},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.448057621717453},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.42552924156188965},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.14511770009994507}],"concepts":[{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.6215720772743225},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5670127272605896},{"id":"https://openalex.org/C77659661","wikidata":"https://www.wikidata.org/wiki/Q448559","display_name":"Crest factor","level":3,"score":0.5218122005462646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5008382797241211},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.48216646909713745},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.47155046463012695},{"id":"https://openalex.org/C66907618","wikidata":"https://www.wikidata.org/wiki/Q207527","display_name":"Sine wave","level":3,"score":0.46467310190200806},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.462862104177475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46126702427864075},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.45286130905151367},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.448057621717453},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.42552924156188965},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.14511770009994507},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/msp.2021.3090681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2021.3090681","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/6e5753d8-da44-4b92-9dfe-03b6c21171a9","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/6e5753d8-da44-4b92-9dfe-03b6c21171a9","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Aarts, R M 2021, 'Tracking and Estimation of Frequency, Amplitude, and Form Factor of a Harmonic Time Series', IEEE Signal Processing Magazine, vol. 38, no. 5, 9524542, pp. 86-91. https://doi.org/10.1109/MSP.2021.3090681","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:publications/6e5753d8-da44-4b92-9dfe-03b6c21171a9","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85190550652&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aarts, R M 2021, 'Tracking and Estimation of Frequency, Amplitude, and Form Factor of a Harmonic Time Series', IEEE Signal Processing Magazine, vol. 38, no. 5, 9524542, pp. 86-91. https://doi.org/10.1109/MSP.2021.3090681","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/6e5753d8-da44-4b92-9dfe-03b6c21171a9","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/6e5753d8-da44-4b92-9dfe-03b6c21171a9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Magazine, 38(5):9524542, 86 - 91. Institute of Electrical and Electronics Engineers","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1967016798","https://openalex.org/W1996348247","https://openalex.org/W2001768493","https://openalex.org/W2083872334","https://openalex.org/W2127379351","https://openalex.org/W2168739331","https://openalex.org/W2594117425","https://openalex.org/W2728047922","https://openalex.org/W2982983009","https://openalex.org/W3010974904","https://openalex.org/W4238906441","https://openalex.org/W6734810431"],"related_works":["https://openalex.org/W2886467464","https://openalex.org/W2063166054","https://openalex.org/W2358475213","https://openalex.org/W2028663913","https://openalex.org/W3142213391","https://openalex.org/W1775321609","https://openalex.org/W2379854577","https://openalex.org/W4385749744","https://openalex.org/W4316092752","https://openalex.org/W2588864086"],"abstract_inverted_index":{"Formulas":[0],"for":[1,53,77,82,104,150],"estimating":[2],"and":[3,10,39,56,115,127,154,172],"tracking":[4,80],"the":[5,27,31,47,51,57,79,100,118,122,169],"(time-dependent)":[6],"frequency,":[7],"form":[8,170],"factor,":[9],"amplitude":[11],"of":[12,50,62,90,121,175],"harmonic":[13],"time":[14],"series":[15],"are":[16,111,148],"presented":[17,109],"in":[18,22,60,113,124],"this":[19],"lecture":[20],"note;":[21],"particular,":[23,131],"sine-dominant":[24,91],"signals,":[25],"where":[26],"harmonics":[28],"follow":[29],"roughly":[30],"dominant":[32],"first":[33],"harmonic,":[34],"such":[35],"as":[36,103],"photoplethysmography":[37],"(PPG)":[38],"breathing":[40],"signals.":[41,84],"Special":[42],"attention":[43],"is":[44,72,133],"paid":[45],"to":[46,65,74,96,136,163],"convergence":[48],"behavior":[49,59],"algorithm":[52],"stationary":[54,67],"signals":[55,92],"dynamic":[58],"case":[61],"a":[63,105,125],"transition":[64],"another":[66],"state.":[68],"The":[69,108],"latter":[70],"issue":[71],"considered":[73],"be":[75,164],"important":[76],"assessing":[78],"abilities":[81],"nonstationary":[83],"We":[85],"will":[86,94],"discuss":[87],"special":[88],"cases":[89],"that":[93],"converge":[95],"an":[97,165],"approximate":[98],"or":[99,140,142],"same":[101],"value":[102],"single":[106],"sinusoid.":[107],"formulas":[110,147],"recursive":[112],"nature":[114],"use":[116,137],"only":[117],"instantaneous":[119],"values":[120],"signal,":[123],"low-cost":[126],"low-complexity":[128],"manner.":[129],"In":[130],"there":[132,161],"no":[134],"need":[135],"square":[138],"roots":[139],"trigonometric":[141],"matrix":[143],"operations;":[144],"therefore,":[145],"these":[146],"suitable":[149],"low-power":[151],"ambulatory":[152],"measurements":[153],"computationally":[155],"demanding":[156],"machine":[157],"learning":[158],"algorithms.":[159],"Furthermore,":[160],"appears":[162],"interesting":[166],"connection":[167],"between":[168],"factor":[171],"Geary's":[173],"test":[174],"normality.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2021-09-13T00:00:00"}
