{"id":"https://openalex.org/W2011379673","doi":"https://doi.org/10.1049/ip-g-1.1988.0012","title":"Number theoretic transforms of periodic structures and their applications","display_name":"Number theoretic transforms of periodic structures and their applications","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W2011379673","doi":"https://doi.org/10.1049/ip-g-1.1988.0012","mag":"2011379673"},"language":"en","primary_location":{"id":"doi:10.1049/ip-g-1.1988.0012","doi":"https://doi.org/10.1049/ip-g-1.1988.0012","is_oa":false,"landing_page_url":"https://doi.org/10.1049/ip-g-1.1988.0012","pdf_url":null,"source":{"id":"https://openalex.org/S4210219774","display_name":"IEE Proceedings G (Electronic Circuits and Systems)","issn_l":"0143-7089","issn":["0143-7089","2053-7964"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEE Proceedings G (Electronic Circuits and Systems)","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5025064240","display_name":"Said Boussakta","orcid":"https://orcid.org/0000-0001-8591-9005","observed_orcids":["https://orcid.org/0000-0001-8591-9005"]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. Boussakta","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","institution_ids":["https://openalex.org/I84884186"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113461392","display_name":"Ali Yeon Md Shakaff","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A.Y. Shakaff","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","institution_ids":["https://openalex.org/I84884186"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113492167","display_name":"Farhi Marir","orcid":"https://orcid.org/0000-0002-8014-5693","observed_orcids":["https://orcid.org/0000-0002-8014-5693"]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"F. Marir","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","institution_ids":["https://openalex.org/I84884186"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012190721","display_name":"A.G.J. Holt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A.G.J. Holt","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, UK","institution_ids":["https://openalex.org/I84884186"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Newcastle-Upon-Tyne Univ., UK","institution_ids":["https://openalex.org/I84884186"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84884186"],"apc_list":null,"apc_paid":null,"fwci":0.7868,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.72294887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"135","issue":"2","first_page":"83","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.6592000126838684,"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":0.6592000126838684,"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":0.15860000252723694,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.05689999833703041,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/number-theoretic-transform","display_name":"number theoretic transform","score":0.921999990940094},{"id":"https://openalex.org/keywords/fermat-number-transform","display_name":"Fermat number transform","score":0.8619999885559082},{"id":"https://openalex.org/keywords/periodic-data","display_name":"periodic data","score":0.9490000009536743},{"id":"https://openalex.org/keywords/image-compression","display_name":"image compression","score":0.7429999709129333},{"id":"https://openalex.org/keywords/data-storage","display_name":"data storage","score":0.9459999799728394},{"id":"https://openalex.org/keywords/image-defects","display_name":"image defects","score":0.7269999980926514},{"id":"https://openalex.org/keywords/error-detection","display_name":"error detection","score":0.8220000267028809},{"id":"https://openalex.org/keywords/industrial-inspection","display_name":"industrial inspection","score":0.675000011920929},{"id":"https://openalex.org/keywords/defect-detection","display_name":"defect detection","score":0.800000011920929}],"concepts":[{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.7104915976524353},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.6155346035957336},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5519407391548157},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5475720167160034},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5007967948913574},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.4978630542755127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4839363694190979},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.44965696334838867},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3573644757270813},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35201162099838257},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23117578029632568},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.169931560754776},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14376604557037354},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1049/ip-g-1.1988.0012","doi":"https://doi.org/10.1049/ip-g-1.1988.0012","is_oa":false,"landing_page_url":"https://doi.org/10.1049/ip-g-1.1988.0012","pdf_url":null,"source":{"id":"https://openalex.org/S4210219774","display_name":"IEE Proceedings G (Electronic Circuits and Systems)","issn_l":"0143-7089","issn":["0143-7089","2053-7964"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEE Proceedings G (Electronic Circuits and Systems)","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1528140240","https://openalex.org/W2020141429","https://openalex.org/W6836002761"],"related_works":["https://openalex.org/W2577599104","https://openalex.org/W2216822875","https://openalex.org/W2113994308","https://openalex.org/W2167752536","https://openalex.org/W1513582003","https://openalex.org/W2103418584","https://openalex.org/W2538475224","https://openalex.org/W2219567307","https://openalex.org/W2185921005","https://openalex.org/W2133355175"],"abstract_inverted_index":{"The":[0],"properties":[1],"of":[2,7,31,61,92],"the":[3,28,36,59,70,76,90],"Fermat":[4],"number":[5,30],"transforms":[6],"periodic":[8],"data":[9,37,52,72],"are":[10,25,43,87],"investigated":[11],"and":[12,39,45,51,100],"it":[13],"is":[14,55],"shown":[15,57],"they":[16],"have":[17],"regular":[18,81],"structures":[19],"with":[20],"many":[21],"zero-valued":[22],"elements.":[23],"Expressions":[24],"derived":[26],"for":[27,48,84,96],"maximum":[29],"nonzero":[32],"elements":[33],"related":[34],"to":[35,89],"row":[38],"column":[40],"periods.":[41],"Examples":[42],"given":[44],"applications":[46],"suggested":[47,88],"image":[49,71],"compression":[50],"storage.":[53],"It":[54],"also":[56],"that":[58],"effects":[60,74],"defects":[62],"as":[63,65],"small":[64],"a":[66],"single":[67],"pixel":[68],"in":[69,94,103],"produce":[73],"upon":[75],"FNT,":[77],"completely":[78],"altering":[79],"its":[80],"structure.":[82],"Applications":[83],"this":[85],"result":[86],"detection":[91,102],"errors":[93],"maskmaking":[95],"integrated":[97],"circuit":[98],"design":[99],"defect":[101],"industrial":[104],"inspection.":[105]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
