{"id":"https://openalex.org/W3171605879","doi":"https://doi.org/10.1109/access.2021.3085515","title":"Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters","display_name":"Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3171605879","doi":"https://doi.org/10.1109/access.2021.3085515","mag":"3171605879"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3085515","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3085515","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09445054.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09445054.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074377437","display_name":"Shibendu Mahata","orcid":"https://orcid.org/0000-0002-8197-6413"},"institutions":[{"id":"https://openalex.org/I155837530","display_name":"National Institute of Technology Durgapur","ror":"https://ror.org/04ds0jm32","country_code":"IN","type":"education","lineage":["https://openalex.org/I155837530"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shibendu Mahata","raw_affiliation_strings":["Dr. B. C. Roy Engineering College, Durgapur, India"],"raw_orcid":"https://orcid.org/0000-0002-8197-6413","affiliations":[{"raw_affiliation_string":"Dr. B. C. Roy Engineering College, Durgapur, India","institution_ids":["https://openalex.org/I155837530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062682055","display_name":"Norbert Herencs\u00e1r","orcid":"https://orcid.org/0000-0002-9504-2275"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Norbert Herencsar","raw_affiliation_strings":["Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-9504-2275","affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087163943","display_name":"David Kub\u00e1nek","orcid":"https://orcid.org/0000-0002-0346-0761"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"David Kubanek","raw_affiliation_strings":["Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-0346-0761","affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.6541,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.93317215,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"9","issue":null,"first_page":"81097","last_page":"81114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/butterworth-filter","display_name":"Butterworth filter","score":0.7464880347251892},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5241230130195618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49745848774909973},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4852862060070038},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.41749435663223267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3841531276702881},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3446325361728668},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3277657926082611},{"id":"https://openalex.org/keywords/low-pass-filter","display_name":"Low-pass filter","score":0.30374252796173096},{"id":"https://openalex.org/keywords/prototype-filter","display_name":"Prototype filter","score":0.1939374804496765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13198339939117432}],"concepts":[{"id":"https://openalex.org/C70757512","wikidata":"https://www.wikidata.org/wiki/Q1018162","display_name":"Butterworth filter","level":5,"score":0.7464880347251892},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5241230130195618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49745848774909973},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4852862060070038},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.41749435663223267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3841531276702881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3446325361728668},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3277657926082611},{"id":"https://openalex.org/C44682112","wikidata":"https://www.wikidata.org/wiki/Q918242","display_name":"Low-pass filter","level":3,"score":0.30374252796173096},{"id":"https://openalex.org/C175742284","wikidata":"https://www.wikidata.org/wiki/Q1415537","display_name":"Prototype filter","level":4,"score":0.1939374804496765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13198339939117432},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/access.2021.3085515","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3085515","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09445054.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:https://dspace.vut.cz:11012/200668","is_oa":true,"landing_page_url":"http://hdl.handle.net/11012/200668","pdf_url":"http://hdl.handle.net/11012/200668","source":{"id":"https://openalex.org/S4306400317","display_name":"Brno University of Technology Digital Library (Brno University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60587646","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/I60587646"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:2a8cee4af1824b7695fe677c26c488bf","is_oa":true,"landing_page_url":"https://doaj.org/article/2a8cee4af1824b7695fe677c26c488bf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 81097-81114 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3085515","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3085515","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09445054.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5225489884","display_name":null,"funder_award_id":"19-24585S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3171605879.pdf","grobid_xml":"https://content.openalex.org/works/W3171605879.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W853345322","https://openalex.org/W1968076019","https://openalex.org/W1989773657","https://openalex.org/W1994016223","https://openalex.org/W1994526710","https://openalex.org/W1999008170","https://openalex.org/W2005010408","https://openalex.org/W2020880018","https://openalex.org/W2028419090","https://openalex.org/W2069373269","https://openalex.org/W2092888192","https://openalex.org/W2129380152","https://openalex.org/W2142141400","https://openalex.org/W2155572235","https://openalex.org/W2161411167","https://openalex.org/W2256461866","https://openalex.org/W2277173815","https://openalex.org/W2278453310","https://openalex.org/W2607214667","https://openalex.org/W2613037233","https://openalex.org/W2613351585","https://openalex.org/W2626384831","https://openalex.org/W2765785876","https://openalex.org/W2786160545","https://openalex.org/W2789606085","https://openalex.org/W2801192398","https://openalex.org/W2898561683","https://openalex.org/W2903009465","https://openalex.org/W2904170357","https://openalex.org/W2905688763","https://openalex.org/W2918140510","https://openalex.org/W2918953246","https://openalex.org/W2920793221","https://openalex.org/W2923296734","https://openalex.org/W2950156639","https://openalex.org/W2953239775","https://openalex.org/W2962126882","https://openalex.org/W2970528191","https://openalex.org/W2971361472","https://openalex.org/W2979113354","https://openalex.org/W2984014761","https://openalex.org/W3003479552","https://openalex.org/W3014767698","https://openalex.org/W3041201157","https://openalex.org/W3068627730","https://openalex.org/W3096063283","https://openalex.org/W3106161440","https://openalex.org/W3109277648"],"related_works":["https://openalex.org/W2129944112","https://openalex.org/W4301184722","https://openalex.org/W2371997661","https://openalex.org/W2371118652","https://openalex.org/W2394199916","https://openalex.org/W2358323523","https://openalex.org/W2607190296","https://openalex.org/W3021732117","https://openalex.org/W2380305669","https://openalex.org/W1542085682"],"abstract_inverted_index":{"In":[0],"this":[1,50],"paper,":[2],"a":[3,111],"new":[4],"two-steps":[5],"design":[6,98],"strategy":[7,128],"is":[8,52,160],"introduced":[9,106],"for":[10,58,99],"the":[11,16,22,26,29,36,64,69,89,96,105,117,120,131,134,147],"optimal":[12],"rational":[13],"approximation":[14],"of":[15,25,102,119,133,146],"fractional-order":[17,112,140],"Butterworth":[18,44,80,141,154],"filter.":[19,81],"At":[20],"first,":[21],"weighting":[23],"factors":[24],"summation":[27],"between":[28],"n":[30],"<sup":[31,40,71,122,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32,41,72,123,151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">th</sup>":[33,42,73,152],"-order":[34,43,153],"and":[35,116,165],"(n":[37],"+":[38],"1)":[39],"filters":[45],"are":[46],"optimally":[47],"determined.":[48],"Subsequently,":[49],"model":[51,115],"employed":[53],"as":[54],"an":[55],"initial":[56],"point":[57],"another":[59],"optimization":[60],"routine,":[61],"which":[62],"minimizes":[63],"magnitude-frequency":[65],"error":[66,93],"relative":[67],"to":[68,95,137],"(n+\u03b1)":[70],"-order,":[74],"where":[75],"\u03b1":[76],"\u2208":[77],"(0,":[78],"1),":[79],"The":[82,126,144],"proposed":[83,127,148],"approximant":[84,118],"demonstrates":[85],"improved":[86],"performance":[87,145],"about":[88],"magnitude":[90],"mean":[91],"squared":[92],"compared":[94],"state-of-the-art":[97],"six":[100],"decades":[101],"bandwidth,":[103],"but":[104],"approach":[107],"does":[108],"not":[109],"require":[110],"transfer":[113],"function":[114],"s":[121],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sup>":[124],"operator.":[125],"also":[129],"avoids":[130],"use":[132],"cascading":[135],"technique":[136],"yield":[138],"higher-order":[139],"filter":[142,155],"models.":[143],"1.5":[149],"in":[156],"follow-the-leader":[157],"feedback":[158,175],"topology":[159],"verified":[161],"through":[162],"SPICE":[163],"simulations":[164],"its":[166],"hardware":[167],"implementation":[168],"based":[169],"on":[170],"Analog":[171],"Devices":[172],"AD844AN-type":[173],"current":[174],"operational":[176],"amplifier.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
