{"id":"https://openalex.org/W2116645245","doi":"https://doi.org/10.3390/a2031221","title":"Multiplication Symmetric Convolution Property for Discrete Trigonometric Transforms","display_name":"Multiplication Symmetric Convolution Property for Discrete Trigonometric Transforms","publication_year":2009,"publication_date":"2009-09-22","ids":{"openalex":"https://openalex.org/W2116645245","doi":"https://doi.org/10.3390/a2031221","mag":"2116645245"},"language":"en","primary_location":{"id":"doi:10.3390/a2031221","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031221","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1221/pdf?version=1253613129","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/2/3/1221/pdf?version=1253613129","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003517080","display_name":"Do Nyeon Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Do Nyeon Kim","raw_affiliation_strings":["Department of Electrical Engineering, University of Texas at Arlington, Box 19016 Arlington, TX 76019, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Texas at Arlington, Box 19016 Arlington, TX 76019, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078861665","display_name":"K.R. Rao","orcid":"https://orcid.org/0000-0002-8513-3114"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. R. Rao","raw_affiliation_strings":["Department of Electrical Engineering, University of Texas at Arlington, Box 19016 Arlington, TX 76019, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Texas at Arlington, Box 19016 Arlington, TX 76019, USA","institution_ids":["https://openalex.org/I189196454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003517080"],"corresponding_institution_ids":["https://openalex.org/I189196454"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14910026,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"3","first_page":"1221","last_page":"1231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9991000294685364,"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":0.9991000294685364,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7393808960914612},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.6858228445053101},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6071285009384155},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.5599626898765564},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5514569878578186},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.46653395891189575},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.4604073464870453},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.45621126890182495},{"id":"https://openalex.org/keywords/reciprocity","display_name":"Reciprocity (cultural anthropology)","score":0.4519117772579193},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3935830295085907},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37762629985809326},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3584238886833191},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26671916246414185},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.21904894709587097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16955959796905518},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1335432529449463},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.1098075807094574},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.08158642053604126}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7393808960914612},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.6858228445053101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6071285009384155},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.5599626898765564},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5514569878578186},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.46653395891189575},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.4604073464870453},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.45621126890182495},{"id":"https://openalex.org/C169903001","wikidata":"https://www.wikidata.org/wiki/Q3264987","display_name":"Reciprocity (cultural anthropology)","level":2,"score":0.4519117772579193},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3935830295085907},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37762629985809326},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3584238886833191},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26671916246414185},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.21904894709587097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16955959796905518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1335432529449463},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.1098075807094574},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.08158642053604126},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a2031221","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031221","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1221/pdf?version=1253613129","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:769096594ad54ba6bb1765ffb9c3a199","is_oa":true,"landing_page_url":"https://doaj.org/article/769096594ad54ba6bb1765ffb9c3a199","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 2, Iss 3, Pp 1221-1231 (2009)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a2031221","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031221","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1221/pdf?version=1253613129","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2116645245.pdf","grobid_xml":"https://content.openalex.org/works/W2116645245.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1815188380","https://openalex.org/W1916685473","https://openalex.org/W1972095837","https://openalex.org/W1992316897","https://openalex.org/W1994935087","https://openalex.org/W2002435757","https://openalex.org/W2114375509","https://openalex.org/W2128749318","https://openalex.org/W2138692623","https://openalex.org/W2141311976","https://openalex.org/W2169314156","https://openalex.org/W2480439833","https://openalex.org/W2906826952","https://openalex.org/W3216957337"],"related_works":["https://openalex.org/W1916685473","https://openalex.org/W2055682261","https://openalex.org/W1993363272","https://openalex.org/W2186390138","https://openalex.org/W2790129917","https://openalex.org/W2060035984","https://openalex.org/W2017990332","https://openalex.org/W2093251826","https://openalex.org/W2080337923","https://openalex.org/W1488776355"],"abstract_inverted_index":{"The":[0],"symmetric-convolution":[1,27],"multiplication":[2,26],"(SCM)":[3],"property":[4,29],"of":[5,21,30],"discrete":[6,31],"trigonometric":[7,32],"transforms":[8],"(DTTs)":[9],"based":[10],"on":[11],"unitary":[12],"transform":[13],"matrices":[14],"is":[15,34],"developed.":[16,35],"Then":[17],"as":[18],"the":[19,24],"reciprocity":[20],"this":[22],"property,":[23],"novel":[25],"(MSC)":[28],"transforms,":[33]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
