{"id":"https://openalex.org/W2104770568","doi":"https://doi.org/10.1109/tassp.1986.1164983","title":"The computation of line spectral frequencies using Chebyshev polynomials","display_name":"The computation of line spectral frequencies using Chebyshev polynomials","publication_year":1986,"publication_date":"1986-12-01","ids":{"openalex":"https://openalex.org/W2104770568","doi":"https://doi.org/10.1109/tassp.1986.1164983","mag":"2104770568"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1986.1164983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1986.1164983","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and 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/A5028284188","display_name":"P. Kabal","orcid":null},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]},{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. Kabal","raw_affiliation_strings":["Department of Electrical Engineering, McGill University, Montreal, QUE, Canada","INRS-T\u00e9l\u00e9communications, Universit\u00e9 du Qu\u00e0bec, Verdun, QUE, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"INRS-T\u00e9l\u00e9communications, Universit\u00e9 du Qu\u00e0bec, Verdun, QUE, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024019873","display_name":"R. Ramachandran","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R.P. Ramachandran","raw_affiliation_strings":["Department of Electrical Engineering, McGill University, Montreal, QUE, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0184,"has_fulltext":false,"cited_by_count":217,"citation_normalized_percentile":{"value":0.77708006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"34","issue":"6","first_page":"1419","last_page":"1426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.786159873008728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7248052358627319},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.6591313481330872},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.5304087400436401},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5025386810302734},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.4976804554462433},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.470156192779541},{"id":"https://openalex.org/keywords/trigonometric-polynomial","display_name":"Trigonometric polynomial","score":0.45191532373428345},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4513756334781647},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44845080375671387},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.43825897574424744},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43268460035324097},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40255701541900635},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.24718120694160461},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07265245914459229}],"concepts":[{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.786159873008728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7248052358627319},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.6591313481330872},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5304087400436401},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5025386810302734},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.4976804554462433},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.470156192779541},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.45191532373428345},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4513756334781647},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44845080375671387},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.43825897574424744},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43268460035324097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40255701541900635},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.24718120694160461},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07265245914459229}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tassp.1986.1164983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1986.1164983","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.330.6012","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.6012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.rowan.edu/~ravi/journal/jour_1986_01.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W140628048","https://openalex.org/W222318538","https://openalex.org/W1519698338","https://openalex.org/W1526835377","https://openalex.org/W1619407006","https://openalex.org/W1692258870","https://openalex.org/W2009674825","https://openalex.org/W2022554507","https://openalex.org/W2046941888","https://openalex.org/W2112216139","https://openalex.org/W2147916262","https://openalex.org/W3094114204"],"related_works":["https://openalex.org/W2021099221","https://openalex.org/W2112919228","https://openalex.org/W1988318322","https://openalex.org/W4390947848","https://openalex.org/W4323652453","https://openalex.org/W2136992695","https://openalex.org/W1866822838","https://openalex.org/W2106962382","https://openalex.org/W2382532955","https://openalex.org/W2074316639"],"abstract_inverted_index":{"Line":[0],"spectral":[1,37,64,101,170],"frequencies":[2,38,65,102,171],"provide":[3],"an":[4,106,176,186],"alternate":[5],"parameterization":[6],"of":[7,19,27,71,74,81,83,116,135,137,157,163,168],"the":[8,30,45,59,69,72,87,132,138,155,161,182],"analysis":[9,46],"and":[10,35,127,146],"synthesis":[11],"filters":[12],"used":[13,149],"in":[14,96,125,150,188],"linear":[15],"predictive":[16],"coding":[17],"(LPC)":[18],"speech.":[20],"In":[21],"this":[22],"paper,":[23],"a":[24,93,117,151],"new":[25],"method":[26,142],"converting":[28],"between":[29],"direct":[31],"form":[32,152],"predictor":[33,173],"coefficients":[34,174],"line":[36,63,100,169],"is":[39,48,90,123,128,143],"presented.":[40],"The":[41,62,79,99,120,141,166],"system":[42],"polynomial":[43,54],"for":[44,113],"filter":[47],"converted":[49],"to":[50,130,172],"two":[51,76],"even-order":[52],"symmetric":[53],"with":[55],"interlacing":[56],"roots":[57,73,115],"on":[58,86],"unit":[60,88],"circle.":[61],"are":[66,103],"given":[67],"by":[68,180],"positions":[70],"these":[75,84],"auxiliary":[77],"polynomials.":[78,98,190],"response":[80],"each":[82],"polynomials":[85],"circle":[89],"expressed":[91],"as":[92,185],"series":[94,139],"expansion":[95,187],"Chebyshev":[97,189],"found":[104],"using":[105],"iterative":[107],"root":[108,183],"finding":[109],"algorithm":[110,121,178],"which":[111],"searches":[112],"real":[114,118],"function.":[119],"developed":[122],"simple":[124],"structure":[126],"designed":[129],"constrain":[131],"maximum":[133],"number":[134],"evaluations":[136],"expansions.":[140],"highly":[144],"accurate":[145],"can":[147],"be":[148],"that":[153],"avoids":[154],"storage":[156],"trigonometric":[158,164],"tables":[159],"or":[160],"computation":[162],"functions.":[165],"reconversion":[167],"uses":[175],"efficient":[177],"derived":[179],"expressing":[181],"factors":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
