{"id":"https://openalex.org/W2130327601","doi":"https://doi.org/10.1109/tsp.2008.2010009","title":"Metrics for Power Spectra: An Axiomatic Approach","display_name":"Metrics for Power Spectra: An Axiomatic Approach","publication_year":2008,"publication_date":"2008-12-04","ids":{"openalex":"https://openalex.org/W2130327601","doi":"https://doi.org/10.1109/tsp.2008.2010009","mag":"2130327601"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2008.2010009","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2008.2010009","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","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/A5035194316","display_name":"Tryphon T. Georgiou","orcid":"https://orcid.org/0000-0003-0012-5447"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T.T. Georgiou","raw_affiliation_strings":["Department of Electrical Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. Eng., Univ. of Minnesota, Minneapolis, MN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of Minnesota, Minneapolis, MN","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065730184","display_name":"Johan Karlsson","orcid":"https://orcid.org/0000-0001-5158-9255"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"J. Karlsson","raw_affiliation_strings":["Department of Mathematics Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden","Dept. of Math., R. Inst. of Technol., Stockholm"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Dept. of Math., R. Inst. of Technol., Stockholm","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054746231","display_name":"Mir Shahrouz Takyar","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M.S. Takyar","raw_affiliation_strings":["Department of Electrical Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. Eng., Univ. of Minnesota, Minneapolis, MN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of Minnesota, Minneapolis, MN","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9369,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.95738305,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"57","issue":"3","first_page":"859","last_page":"867"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9628000259399414,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7925100326538086},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6661680936813354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6452465057373047},{"id":"https://openalex.org/keywords/axiomatic-system","display_name":"Axiomatic system","score":0.5994880795478821},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5932864546775818},{"id":"https://openalex.org/keywords/fisher-information-metric","display_name":"Fisher information metric","score":0.48087695240974426},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.4669288992881775},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.44693219661712646},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4414808750152588},{"id":"https://openalex.org/keywords/equivalence-of-metrics","display_name":"Equivalence of metrics","score":0.4201936423778534},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3890463709831238},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3836022913455963},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.30200496315956116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2775244116783142},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.2626814842224121},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23874759674072266},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23266446590423584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2097541093826294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14363142848014832},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.14172905683517456}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7925100326538086},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6661680936813354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6452465057373047},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.5994880795478821},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5932864546775818},{"id":"https://openalex.org/C127104897","wikidata":"https://www.wikidata.org/wiki/Q5454858","display_name":"Fisher information metric","level":4,"score":0.48087695240974426},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.4669288992881775},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.44693219661712646},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4414808750152588},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.4201936423778534},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3890463709831238},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3836022913455963},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.30200496315956116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2775244116783142},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.2626814842224121},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23874759674072266},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23266446590423584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2097541093826294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14363142848014832},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.14172905683517456},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2008.2010009","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2008.2010009","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W85439921","https://openalex.org/W107085514","https://openalex.org/W152055444","https://openalex.org/W158030646","https://openalex.org/W297279189","https://openalex.org/W583356579","https://openalex.org/W646945617","https://openalex.org/W1494145268","https://openalex.org/W1514558801","https://openalex.org/W1573082642","https://openalex.org/W1585160083","https://openalex.org/W1613238992","https://openalex.org/W1669302803","https://openalex.org/W1672262794","https://openalex.org/W1963871118","https://openalex.org/W1966264494","https://openalex.org/W1979610031","https://openalex.org/W1988137251","https://openalex.org/W1989337816","https://openalex.org/W2003001219","https://openalex.org/W2009745852","https://openalex.org/W2022554507","https://openalex.org/W2033468335","https://openalex.org/W2045463928","https://openalex.org/W2045557014","https://openalex.org/W2048435560","https://openalex.org/W2091891040","https://openalex.org/W2099515730","https://openalex.org/W2123838014","https://openalex.org/W2138358404","https://openalex.org/W2156602598","https://openalex.org/W2161585662","https://openalex.org/W2164240509","https://openalex.org/W3098976616","https://openalex.org/W3110683067","https://openalex.org/W4254303765","https://openalex.org/W4388534025","https://openalex.org/W6786768871"],"related_works":["https://openalex.org/W2947185879","https://openalex.org/W2398868469","https://openalex.org/W2001114394","https://openalex.org/W2185831068","https://openalex.org/W2000097109","https://openalex.org/W3018342392","https://openalex.org/W4205383077","https://openalex.org/W2742284041","https://openalex.org/W3157600342","https://openalex.org/W4297851895"],"abstract_inverted_index":{"We":[0,52],"present":[1,54],"an":[2,76],"axiomatic":[3],"framework":[4],"for":[5],"seeking":[6],"distances":[7],"between":[8],"power":[9],"spectral":[10],"density":[11],"functions.":[12],"The":[13,63],"axioms":[14],"require":[15,39],"that":[16],"the":[17,21,50,68,82,87,96,105],"sought":[18],"metric":[19,57,64,79],"respects":[20],"effects":[22],"of":[23,41,86],"additive":[24],"and":[25,72],"multiplicative":[26],"noise":[27],"in":[28,49],"reducing":[29],"our":[30],"ability":[31],"to":[32,46],"discriminate":[33],"spectra,":[34],"as":[35,37,102,104],"well":[36,103],"they":[38],"continuity":[40],"statistical":[42],"quantities":[43],"with":[44,75,95],"respect":[45],"perturbations":[47],"measured":[48],"metric.":[51],"then":[53],"a":[55],"particular":[56],"which":[58],"abides":[59],"by":[60],"these":[61],"requirements.":[62],"is":[65,73,91],"based":[66,80],"on":[67,81,109],"Monge-Kantorovich":[69],"transportation":[70],"problem":[71],"contrasted":[74],"earlier":[77],"Riemannian":[78],"minimum-variance":[83],"prediction":[84,107],"geometry":[85],"underlying":[88],"time-series.":[89],"It":[90],"also":[92],"being":[93],"compared":[94],"more":[97],"traditional":[98],"Itakura-Saito":[99],"distance":[100],"measure,":[101],"aforementioned":[106],"metric,":[108],"two":[110],"representative":[111],"examples.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}