{"id":"https://openalex.org/W4298003808","doi":"https://doi.org/10.3390/sym14102018","title":"Quadratic-Phase Wave-Packet Transform in L2(R)","display_name":"Quadratic-Phase Wave-Packet Transform in L2(R)","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W4298003808","doi":"https://doi.org/10.3390/sym14102018"},"language":"en","primary_location":{"id":"doi:10.3390/sym14102018","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102018","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2018/pdf?version=1666603032","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/2073-8994/14/10/2018/pdf?version=1666603032","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]}],"countries":["AZ","CA","TW"],"is_corresponding":true,"raw_author_name":"Hari M. Srivastava","raw_affiliation_strings":["Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037201286","display_name":"Firdous A. Shah","orcid":"https://orcid.org/0000-0001-8461-869X"},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Firdous A. Shah","raw_affiliation_strings":["Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India"],"raw_orcid":"https://orcid.org/0000-0001-8461-869X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India","institution_ids":["https://openalex.org/I135388327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068911437","display_name":"Waseem Z. Lone","orcid":"https://orcid.org/0000-0002-9826-9475"},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Waseem Z. Lone","raw_affiliation_strings":["Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India"],"raw_orcid":"https://orcid.org/0000-0002-9826-9475","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India","institution_ids":["https://openalex.org/I135388327"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5079512627"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I212119943","https://openalex.org/I4210126829","https://openalex.org/I87490745"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.057,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86568394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"10","first_page":"2018","last_page":"2018"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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":0.9995999932289124,"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/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/s-transform","display_name":"S transform","score":0.6684730648994446},{"id":"https://openalex.org/keywords/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.6224423050880432},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5895951986312866},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.5811324715614319},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.5158571600914001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5108318328857422},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4819302558898926},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4625477194786072},{"id":"https://openalex.org/keywords/wave-packet","display_name":"Wave packet","score":0.4595580995082855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45661869645118713},{"id":"https://openalex.org/keywords/constant-q-transform","display_name":"Constant Q transform","score":0.4338873028755188},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.42298638820648193},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4213874340057373},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3639742434024811},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31455105543136597},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.19644895195960999},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16092762351036072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13663777709007263},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07924607396125793}],"concepts":[{"id":"https://openalex.org/C99234102","wikidata":"https://www.wikidata.org/wiki/Q7395403","display_name":"S transform","level":5,"score":0.6684730648994446},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.6224423050880432},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5895951986312866},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.5811324715614319},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.5158571600914001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5108318328857422},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4819302558898926},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4625477194786072},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.4595580995082855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45661869645118713},{"id":"https://openalex.org/C153705960","wikidata":"https://www.wikidata.org/wiki/Q5163634","display_name":"Constant Q transform","level":5,"score":0.4338873028755188},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.42298638820648193},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4213874340057373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3639742434024811},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31455105543136597},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.19644895195960999},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16092762351036072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13663777709007263},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07924607396125793},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14102018","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102018","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2018/pdf?version=1666603032","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:8ff0900868dd46f5bb5763dcb63ef686","is_oa":true,"landing_page_url":"https://doaj.org/article/8ff0900868dd46f5bb5763dcb63ef686","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 10, p 2018 (2022)","raw_type":"article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/14393","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/14393","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/2018/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14102018","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/sym14102018","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102018","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2018/pdf?version=1666603032","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.699999988079071}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4298003808.pdf","grobid_xml":"https://content.openalex.org/works/W4298003808.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965595165","https://openalex.org/W2032249561","https://openalex.org/W2341428437","https://openalex.org/W2479221532","https://openalex.org/W2751843979","https://openalex.org/W2782129828","https://openalex.org/W2884790150","https://openalex.org/W2891681470","https://openalex.org/W2964033081","https://openalex.org/W2994434658","https://openalex.org/W3127982291","https://openalex.org/W3192455865","https://openalex.org/W3206678275","https://openalex.org/W3215478101","https://openalex.org/W4288901815","https://openalex.org/W6802421889"],"related_works":["https://openalex.org/W2222331773","https://openalex.org/W237185286","https://openalex.org/W2045970078","https://openalex.org/W2110959724","https://openalex.org/W19668000","https://openalex.org/W2390879839","https://openalex.org/W2378148381","https://openalex.org/W4391265621","https://openalex.org/W2551275593","https://openalex.org/W2048730702"],"abstract_inverted_index":{"Wavelet":[0],"transform":[1,55,61,66,74,80,127],"is":[2,35,67],"a":[3,52,77,108],"powerful":[4],"tool":[5],"for":[6,29],"analysing":[7],"the":[8,40,71,87,91,95,101,112,117,124,129,138,141,146],"problems":[9],"arising":[10],"in":[11,39,62,128],"harmonic":[12],"analysis,":[13],"signal":[14],"and":[15,20,100,116],"image":[16],"processing,":[17],"sampling,":[18],"filtering,":[19],"so":[21],"on.":[22],"However,":[23],"they":[24],"seem":[25],"to":[26],"be":[27],"inadequate":[28],"representing":[30],"those":[31],"signals":[32],"whose":[33],"energy":[34],"not":[36],"well":[37],"concentrated":[38],"frequency":[41],"domain.":[42],"In":[43,120],"pursuit":[44],"of":[45,47,84,89,103,131,140,148],"representations":[46],"such":[48],"signals,":[49],"we":[50,105,122,136],"propose":[51],"novel":[53],"time-frequency":[54],"coined":[56],"as":[57],"quadratic-phase":[58,78,125,149],"wave":[59,150],"packet":[60,151],"L2(R).":[63],"The":[64],"proposed":[65,118],"aimed":[68],"at":[69],"rectifying":[70],"conventional":[72],"wavelet":[73],"by":[75,144],"employing":[76],"Fourier":[79],"with":[81],"extra":[82],"degrees":[83],"freedom.":[85],"Besides":[86],"formulation":[88],"all":[90],"fundamental":[92],"results,":[93],"including":[94],"orthogonality":[96],"relation,":[97],"reconstruction":[98],"formula":[99],"characterization":[102],"range,":[104],"also":[106],"derive":[107],"direct":[109],"relationship":[110],"between":[111],"well-known":[113],"Wigner-Ville":[114],"distribution":[115],"transform.":[119],"addition,":[121],"study":[123],"wave-packet":[126],"framework":[130],"almost":[132],"periodic":[133],"functions.":[134],"Finally,":[135],"extend":[137],"scope":[139],"present":[142],"work":[143],"investigating":[145],"composition":[147],"transforms.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
