{"id":"https://openalex.org/W4285009541","doi":"https://doi.org/10.3390/sym14071416","title":"Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach","display_name":"Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach","publication_year":2022,"publication_date":"2022-07-10","ids":{"openalex":"https://openalex.org/W4285009541","doi":"https://doi.org/10.3390/sym14071416"},"language":"en","primary_location":{"id":"doi:10.3390/sym14071416","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071416","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1416/pdf?version=1658387237","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/2073-8994/14/7/1416/pdf?version=1658387237","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043368707","display_name":"M. Younus Bhat","orcid":"https://orcid.org/0000-0002-3369-0883"},"institutions":[{"id":"https://openalex.org/I4264650","display_name":"Islamic University of Science and Technology","ror":"https://ror.org/02kdtt649","country_code":"IN","type":"education","lineage":["https://openalex.org/I4264650"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Mohammad Younus Bhat","raw_affiliation_strings":["Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"],"raw_orcid":"https://orcid.org/0000-0002-3369-0883","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India","institution_ids":["https://openalex.org/I4264650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072000208","display_name":"Badr Alnssyan","orcid":"https://orcid.org/0000-0003-1541-6239"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Badr Alnssyan","raw_affiliation_strings":["Department of Administrative Sciences and Humanities, Applied College, Qassim University, Buraydah 51452, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1541-6239","affiliations":[{"raw_affiliation_string":"Department of Administrative Sciences and Humanities, Applied College, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016457546","display_name":"Aamir H. Dar","orcid":"https://orcid.org/0000-0001-5124-2761"},"institutions":[{"id":"https://openalex.org/I4264650","display_name":"Islamic University of Science and Technology","ror":"https://ror.org/02kdtt649","country_code":"IN","type":"education","lineage":["https://openalex.org/I4264650"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Aamir H. Dar","raw_affiliation_strings":["Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"],"raw_orcid":"https://orcid.org/0000-0001-5124-2761","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India","institution_ids":["https://openalex.org/I4264650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027980310","display_name":"Javid Gani Dar","orcid":"https://orcid.org/0000-0002-7565-2244"},"institutions":[{"id":"https://openalex.org/I4264650","display_name":"Islamic University of Science and Technology","ror":"https://ror.org/02kdtt649","country_code":"IN","type":"education","lineage":["https://openalex.org/I4264650"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Javid G. Dar","raw_affiliation_strings":["Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India","institution_ids":["https://openalex.org/I4264650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043368707"],"corresponding_institution_ids":["https://openalex.org/I4264650"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0979,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.34799795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"7","first_page":"1416","last_page":"1416"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.989300012588501,"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":0.989300012588501,"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/T10573","display_name":"Power Quality and Harmonics","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9782000184059143,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/aliasing","display_name":"Aliasing","score":0.662418007850647},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5706886053085327},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5573787689208984},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5539987683296204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5051677823066711},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5029045939445496},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.4772850573062897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45825493335723877},{"id":"https://openalex.org/keywords/oversampling","display_name":"Oversampling","score":0.42975887656211853},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3609687089920044},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35029634833335876},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15721413493156433},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.15239578485488892},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1471477746963501}],"concepts":[{"id":"https://openalex.org/C4069607","wikidata":"https://www.wikidata.org/wiki/Q868732","display_name":"Aliasing","level":3,"score":0.662418007850647},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5706886053085327},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5573787689208984},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5539987683296204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5051677823066711},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5029045939445496},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.4772850573062897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45825493335723877},{"id":"https://openalex.org/C197323446","wikidata":"https://www.wikidata.org/wiki/Q331222","display_name":"Oversampling","level":3,"score":0.42975887656211853},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3609687089920044},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35029634833335876},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15721413493156433},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15239578485488892},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1471477746963501},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C136536468","wikidata":"https://www.wikidata.org/wiki/Q1225894","display_name":"Undersampling","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14071416","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071416","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1416/pdf?version=1658387237","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:18ed6841a5af47aa9c420e9df88be319","is_oa":true,"landing_page_url":"https://doaj.org/article/18ed6841a5af47aa9c420e9df88be319","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 14, Iss 7, p 1416 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/7/1416/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14071416","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/sym14071416","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071416","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1416/pdf?version=1658387237","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285009541.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1965160907","https://openalex.org/W1967276951","https://openalex.org/W1986754283","https://openalex.org/W2005286627","https://openalex.org/W2114126736","https://openalex.org/W2116479736","https://openalex.org/W2136567725","https://openalex.org/W2147621019","https://openalex.org/W2170014524","https://openalex.org/W2170182872","https://openalex.org/W2652471884","https://openalex.org/W2750375755","https://openalex.org/W2922231589","https://openalex.org/W2937801808","https://openalex.org/W2987808291","https://openalex.org/W2989151353","https://openalex.org/W3104555676","https://openalex.org/W3148676806","https://openalex.org/W3199409609","https://openalex.org/W3200022538","https://openalex.org/W3204636293","https://openalex.org/W3205338827","https://openalex.org/W3217024661","https://openalex.org/W4238865235","https://openalex.org/W6677108371","https://openalex.org/W6801606504","https://openalex.org/W6802076489","https://openalex.org/W6804285173","https://openalex.org/W6820478434"],"related_works":["https://openalex.org/W2766503024","https://openalex.org/W2781247653","https://openalex.org/W2100912434","https://openalex.org/W2152863486","https://openalex.org/W2046664308","https://openalex.org/W2996441418","https://openalex.org/W1970010277","https://openalex.org/W4286614785","https://openalex.org/W3084192357","https://openalex.org/W2387422968"],"abstract_inverted_index":{"A":[0],"linear":[1],"canonical":[2],"S":[3],"transform":[4,13],"(LCST)":[5],"is":[6,29,106],"considered":[7],"a":[8,45,66,99],"generalization":[9],"of":[10,65,86,102],"the":[11,41,56,60,63,74,80],"Stockwell":[12],"(ST).":[14],"It":[15,37],"analyzes":[16],"signals":[17],"and":[18,23,76],"has":[19],"multi-angle,":[20],"multi-scale,":[21],"multiresolution,":[22],"temporal":[24],"localization":[25],"abilities.":[26],"The":[27],"LCST":[28,61],"mostly":[30],"suitable":[31],"to":[32,39,54],"deal":[33],"with":[34,62],"chirp-like":[35],"signals.":[36],"aims":[38],"possess":[40],"characteristics":[42],"lacking":[43],"in":[44,50,98],"classical":[46],"transform.":[47],"Our":[48],"aim":[49],"this":[51],"paper":[52],"was":[53],"derive":[55],"sampling":[57,82,87],"theorem":[58],"for":[59,79,93],"help":[64],"multiresolution":[67],"analysis":[68],"(MRA)":[69],"approach.":[70],"Moreover,":[71],"we":[72],"discuss":[73],"truncation":[75],"aliasing":[77],"errors":[78],"proposed":[81],"theory.":[83],"These":[84],"types":[85],"results,":[88],"as":[89,91],"well":[90],"methodologies":[92],"solving":[94],"them,":[95],"have":[96],"applications":[97],"wide":[100],"range":[101],"fields":[103],"where":[104],"symmetry":[105],"crucial.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
