{"id":"https://openalex.org/W7161110040","doi":"https://doi.org/10.1109/lsp.2026.3693202","title":"On the Convergence of the Fast Griffin-Lim Algorithm","display_name":"On the Convergence of the Fast Griffin-Lim Algorithm","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7161110040","doi":"https://doi.org/10.1109/lsp.2026.3693202"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2026.3693202","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3693202","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Letters","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/A5000588289","display_name":"Alessandro Ilic Mezza","orcid":"https://orcid.org/0000-0002-9438-3190"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Ilic Mezza","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9438-3190","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066131437","display_name":"Massimo Cicognani","orcid":null},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimo Cicognani","raw_affiliation_strings":["Dipartimento di Matematica, Università di Bologna, Bologna, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Università di Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136134921","display_name":"Roberto Leone Cicognani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roberto Leone Cicognani","raw_affiliation_strings":["Korg Italy, Osimo, Italy"],"raw_orcid":"https://orcid.org/0009-0004-9254-4570","affiliations":[{"raw_affiliation_string":"Korg Italy, Osimo, Italy","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088704369","display_name":"Alberto Bernardini","orcid":"https://orcid.org/0000-0001-7973-0134"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Bernardini","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7973-0134","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58664176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":null,"first_page":"2006","last_page":"2010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.07829999923706055,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.07829999923706055,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.07320000231266022,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.04320000112056732,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/convergence","display_name":"Convergence (economics)","score":0.664900004863739},{"id":"https://openalex.org/keywords/algorithm-design","display_name":"Algorithm design","score":0.4311000108718872},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.34549999237060547},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.3276999890804291},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.32109999656677246},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.2840999960899353}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.664900004863739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5861999988555908},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5636000037193298},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3528999984264374},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.313400000333786},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.28380000591278076},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C2988922011","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering theory","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2026.3693202","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3693202","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Letters","raw_type":"journal-article"},{"id":"pmh:oai:cris.unibo.it:11585/1063450","is_oa":false,"landing_page_url":"https://hdl.handle.net/11585/1063450","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Fast":[1],"Griffin-Lim":[2,28],"Algorithm":[3,29],"(FGLA)":[4],"is":[5,128],"one":[6],"of":[7,34,68,112],"the":[8,26,32,66,69,132],"most":[9],"widely":[10],"used":[11],"iterative":[12],"methods":[13],"for":[14,48],"phase":[15],"reconstruction":[16],"and":[17,74,76,114],"signal":[18],"estimation":[19],"from":[20],"modified":[21],"short-time":[22],"Fourier":[23],"transforms.":[24],"Unlike":[25],"classic":[27],"(GLA),":[30],"however,":[31],"convergence":[33,107],"FGLA":[35,89],"has":[36],"not":[37],"yet":[38],"been":[39],"fully":[40],"proved,":[41],"with":[42,97],"existing":[43],"theoretical":[44],"guarantees":[45],"holding":[46],"only":[47],"momenta":[49,113],"significantly":[50],"smaller":[51],"than":[52],"those":[53],"found":[54],"to":[55,91,118],"perform":[56],"best":[57],"in":[58,122],"practice.":[59],"In":[60],"this":[61],"letter,":[62],"we":[63,86,126],"build":[64],"upon":[65],"appendix":[67],"original":[70],"paper":[71],"by":[72],"Griffin":[73],"Lim":[75],"formulate":[77,115],"GLA":[78],"as":[79],"a":[80,103,109,116],"gradient":[81,94],"descent":[82,95],"algorithm.":[83],"From":[84],"this,":[85],"show":[87],"that":[88],"corresponds":[90],"an":[92],"accelerated":[93],"method":[96],"constant":[98],"momentum.":[99],"We":[100],"then":[101],"derive":[102],"sufficient":[104],"condition":[105],"ensuring":[106],"over":[108],"broad":[110],"range":[111],"criterion":[117],"assess":[119],"its":[120],"validity":[121],"numerical":[123],"experiments,":[124],"which":[125],"find":[127],"typically":[129],"satisfied":[130],"within":[131],"first":[133],"few":[134],"iterations.":[135]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-05-15T00:00:00"}