{"id":"https://openalex.org/W2137734510","doi":"https://doi.org/10.1109/tassp.1987.1165202","title":"A two-stage representation of DFT and its applications","display_name":"A two-stage representation of DFT and its applications","publication_year":1987,"publication_date":"1987-06-01","ids":{"openalex":"https://openalex.org/W2137734510","doi":"https://doi.org/10.1109/tassp.1987.1165202","mag":"2137734510"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1987.1165202","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1987.1165202","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/A5083478920","display_name":"Okan K. Ersoy","orcid":"https://orcid.org/0000-0002-7626-0584"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"O. Ersoy","raw_affiliation_strings":["School of Electrical Engineering, Purdue University, West Lafayette, IN, USA","Purdue Univ., West LaFayette, IN"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue Univ., West LaFayette, IN","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083478920"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":3.5404,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.92933619,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"6","first_page":"825","last_page":"831"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9990000128746033,"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":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5213481187820435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4143053889274597},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38748276233673096},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38672614097595215},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3777329921722412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2834351658821106}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5213481187820435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4143053889274597},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38748276233673096},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38672614097595215},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3777329921722412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2834351658821106},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tassp.1987.1165202","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1987.1165202","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W116047052","https://openalex.org/W1563104231","https://openalex.org/W1982628855","https://openalex.org/W1985765205","https://openalex.org/W1997654368","https://openalex.org/W2006000667","https://openalex.org/W2011425197","https://openalex.org/W2031333467","https://openalex.org/W2054326086","https://openalex.org/W2074917673","https://openalex.org/W2078104849","https://openalex.org/W2095137999","https://openalex.org/W2113994308","https://openalex.org/W2169691387","https://openalex.org/W4254389654"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"A":[0],"two-stage":[1,103],"representation":[2,104],"in":[3,110],"terms":[4],"of":[5,9,16,27,97,116],"preprocessing":[6,31],"and":[7,18,37,49,66,95,118],"postprocessing":[8,83],"DFT":[10,117],"is":[11,39,76,85,91],"developed":[12],"by":[13,41,56],"vector":[14],"transformation":[15],"sines":[17],"cosines":[19],"into":[20],"new":[21,99],"basis":[22,100],"functions":[23],"using":[24],"M\u00f6bius":[25],"inversion":[26],"number":[28],"theory.":[29],"The":[30,82,102],"matrix,":[32],"with":[33],"elements":[34],"1,":[35],"-1,":[36],"0,":[38],"obtained":[40],"replacing":[42],"<tex":[43,50,57,67,73],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[44,51,58,68,74],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\cos":[45],"2\\pin":[46,53],"/":[47,54,60,64],"N</tex>":[48,55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\sin":[52],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\mu(n":[59],"N":[61],"+":[62],"1":[63],"4)</tex>":[65],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\mu(n/N)</tex>":[69],",":[70],"respectively,":[71],"where":[72,88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\mu(\\cdot)</tex>":[75],"the":[77,98],"bipolar":[78],"rectangular":[79],"wave":[80],"function.":[81],"matrix":[84],"block":[86,90],"diagonal":[87],"each":[89],"a":[92],"circular":[93],"correlation":[94],"consists":[96],"functions.":[101],"has":[105],"been":[106],"found":[107],"very":[108],"useful":[109],"applications":[111],"such":[112],"as":[113],"parallel":[114],"implementation":[115],"signal/image":[119],"recognition.":[120]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
