{"id":"https://openalex.org/W2795902834","doi":"https://doi.org/10.3390/sym10040101","title":"A Framework for Circular Multilevel Systems in the Frequency Domain","display_name":"A Framework for Circular Multilevel Systems in the Frequency Domain","publication_year":2018,"publication_date":"2018-04-08","ids":{"openalex":"https://openalex.org/W2795902834","doi":"https://doi.org/10.3390/sym10040101","mag":"2795902834"},"language":"en","primary_location":{"id":"doi:10.3390/sym10040101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10040101","pdf_url":"https://www.mdpi.com/2073-8994/10/4/101/pdf?version=1525347598","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/4/101/pdf?version=1525347598","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046378655","display_name":"Guomin Sun","orcid":"https://orcid.org/0000-0003-4655-8571"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guomin Sun","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":"https://orcid.org/0000-0003-4655-8571","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108338888","display_name":"Jinsong Leng","orcid":"https://orcid.org/0000-0001-5985-5730"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinsong Leng","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022405104","display_name":"Carlo Cattani","orcid":"https://orcid.org/0000-0002-7504-0424"},"institutions":[{"id":"https://openalex.org/I138938424","display_name":"Universit\u00e0 degli Studi della Tuscia","ror":"https://ror.org/03svwq685","country_code":"IT","type":"education","lineage":["https://openalex.org/I138938424"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carlo Cattani","raw_affiliation_strings":["Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7504-0424","affiliations":[{"raw_affiliation_string":"Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy","institution_ids":["https://openalex.org/I138938424"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022405104","https://openalex.org/A5046378655"],"corresponding_institution_ids":["https://openalex.org/I138938424","https://openalex.org/I150229711"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2434,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.54980627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"10","issue":"4","first_page":"101","last_page":"101"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9997000098228455,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9897000193595886,"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/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.6437609195709229},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6302727460861206},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5871427655220032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5636167526245117},{"id":"https://openalex.org/keywords/non-uniform-discrete-fourier-transform","display_name":"Non-uniform discrete Fourier transform","score":0.5004744529724121},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.4592558741569519},{"id":"https://openalex.org/keywords/discrete-time-fourier-transform","display_name":"Discrete-time Fourier transform","score":0.4562554955482483},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4546140432357788},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.44568905234336853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4257062077522278},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.4183550477027893},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.41420263051986694},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38092491030693054},{"id":"https://openalex.org/keywords/short-time-fourier-transform","display_name":"Short-time Fourier transform","score":0.3506576418876648},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25109368562698364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10829567909240723}],"concepts":[{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.6437609195709229},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6302727460861206},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5871427655220032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5636167526245117},{"id":"https://openalex.org/C62058723","wikidata":"https://www.wikidata.org/wiki/Q7049066","display_name":"Non-uniform discrete Fourier transform","level":5,"score":0.5004744529724121},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.4592558741569519},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.4562554955482483},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4546140432357788},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.44568905234336853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4257062077522278},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.4183550477027893},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.41420263051986694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38092491030693054},{"id":"https://openalex.org/C166386157","wikidata":"https://www.wikidata.org/wiki/Q1477735","display_name":"Short-time Fourier transform","level":4,"score":0.3506576418876648},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25109368562698364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10829567909240723}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10040101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10040101","pdf_url":"https://www.mdpi.com/2073-8994/10/4/101/pdf?version=1525347598","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e36a65f8e1ca46c083700481b98d815d","is_oa":true,"landing_page_url":"https://doaj.org/article/e36a65f8e1ca46c083700481b98d815d","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":"Symmetry, Vol 10, Iss 4, p 101 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/4/101/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym10040101","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym10040101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10040101","pdf_url":"https://www.mdpi.com/2073-8994/10/4/101/pdf?version=1525347598","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1985492840","https://openalex.org/W2026752606","https://openalex.org/W2034741500","https://openalex.org/W2045849979","https://openalex.org/W2068419241","https://openalex.org/W2069912449","https://openalex.org/W2072084087","https://openalex.org/W2078498319","https://openalex.org/W2085744431","https://openalex.org/W2086554260","https://openalex.org/W2094411763","https://openalex.org/W2103030298","https://openalex.org/W2117853853","https://openalex.org/W2126388635","https://openalex.org/W2132984323","https://openalex.org/W4247341659","https://openalex.org/W4254902779","https://openalex.org/W6635986890","https://openalex.org/W6671838127","https://openalex.org/W6674178327"],"related_works":["https://openalex.org/W4232826315","https://openalex.org/W2900642428","https://openalex.org/W1967434260","https://openalex.org/W1281595","https://openalex.org/W2002136255","https://openalex.org/W1440546804","https://openalex.org/W19668000","https://openalex.org/W3021127325","https://openalex.org/W2149419755","https://openalex.org/W2377922705"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"will":[4],"construct":[5],"a":[6,54,73,133,145,159],"new":[7,74,154],"multilevel":[8,46,170],"system":[9,47,171],"in":[10,136,187],"the":[11,15,49,57,64,70,79,87,110,117,128,137,141,153,166,174,182,188],"Fourier":[12,90,130,156,161,189],"domain":[13,59,139],"using":[14],"harmonic":[16,22,167],"wavelet.":[17,43],"The":[18,44,92,106,148],"main":[19,107],"advantages":[20],"of":[21,56,76,95,184],"wavelet":[23,66,168],"are":[24,103],"that":[25,127],"its":[26,37],"frequency":[27,58,138],"spectrum":[28],"is":[29,83,116,126,178],"confined":[30],"exactly":[31],"to":[32],"an":[33],"octave":[34],"band,":[35],"and":[36,62,85,114,152],"simple":[38],"definition":[39],"just":[40],"as":[41],"Haar":[42],"constructed":[45],"has":[48,132,144],"circular":[50,71,134],"shape,":[51,72],"which":[52],"forms":[53],"partition":[55],"by":[60],"shifting":[61],"scaling":[63],"basic":[65],"functions.":[67],"To":[68],"possess":[69],"type":[75],"sampling":[77,119,150,176],"grid,":[78],"circular-polar":[80],"grid":[81,113,151,177],"(CPG),":[82],"defined":[84,155,172],"also":[86],"corresponding":[88],"modified":[89,129],"transform.":[91],"CPG":[93,115],"consists":[94],"equal":[96],"space":[97],"along":[98],"rays,":[99],"where":[100],"different":[101],"rays":[102],"equally":[104],"angled.":[105],"difference":[108,125],"between":[109],"classic":[111],"polar":[112,121,142],"even":[118],"on":[120,173],"coordinates.":[122],"Another":[123],"obvious":[124],"transform":[131,143,157,162],"shape":[135],"while":[140],"square":[146],"shape.":[147],"proposed":[149,175],"constitute":[158],"completely":[160],"system,":[163],"more":[164,179],"importantly,":[165],"based":[169],"suitable":[180],"for":[181],"distribution":[183],"general":[185],"images":[186],"domain.":[190]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
