{"id":"https://openalex.org/W1979842022","doi":"https://doi.org/10.1137/s0036139900379638","title":"Periodic Wavelet Transforms and Periodicity Detection","display_name":"Periodic Wavelet Transforms and Periodicity Detection","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1979842022","doi":"https://doi.org/10.1137/s0036139900379638","mag":"1979842022"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139900379638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900379638","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","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/A5011675506","display_name":"G\u00f6tz E. Pfander","orcid":"https://orcid.org/0000-0002-2521-0755"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G\u00f6tz E. Pfander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088060405","display_name":"John J. Benedetto","orcid":"https://orcid.org/0000-0003-0257-6401"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John J. Benedetto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6463,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.79908427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"4","first_page":"1329","last_page":"1368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9919999837875366,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.8781758546829224},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.7151371240615845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7003316879272461},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.6130956411361694},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.6085985898971558},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5589322447776794},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5021109580993652},{"id":"https://openalex.org/keywords/fast-wavelet-transform","display_name":"Fast wavelet transform","score":0.4857092797756195},{"id":"https://openalex.org/keywords/cascade-algorithm","display_name":"Cascade algorithm","score":0.4699649512767792},{"id":"https://openalex.org/keywords/stationary-wavelet-transform","display_name":"Stationary wavelet transform","score":0.44389963150024414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4270833134651184},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38634034991264343},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3533811569213867},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35329049825668335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22760513424873352},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13279631733894348}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.8781758546829224},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.7151371240615845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7003316879272461},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.6130956411361694},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.6085985898971558},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5589322447776794},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5021109580993652},{"id":"https://openalex.org/C132736078","wikidata":"https://www.wikidata.org/wiki/Q338438","display_name":"Fast wavelet transform","level":5,"score":0.4857092797756195},{"id":"https://openalex.org/C88829872","wikidata":"https://www.wikidata.org/wiki/Q5048176","display_name":"Cascade algorithm","level":5,"score":0.4699649512767792},{"id":"https://openalex.org/C73339587","wikidata":"https://www.wikidata.org/wiki/Q1375942","display_name":"Stationary wavelet transform","level":5,"score":0.44389963150024414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4270833134651184},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38634034991264343},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3533811569213867},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35329049825668335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22760513424873352},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13279631733894348}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139900379638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900379638","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.6034","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.6034","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.jacobs-university.de/pfander/phdthesis.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W63201508","https://openalex.org/W64449840","https://openalex.org/W164002609","https://openalex.org/W1520187819","https://openalex.org/W1532132626","https://openalex.org/W1559907478","https://openalex.org/W1597732836","https://openalex.org/W1942844062","https://openalex.org/W1983378326","https://openalex.org/W1992244412","https://openalex.org/W1998566737","https://openalex.org/W2016895710","https://openalex.org/W2019409774","https://openalex.org/W2029500619","https://openalex.org/W2035180855","https://openalex.org/W2039078035","https://openalex.org/W2062024414","https://openalex.org/W2062890119","https://openalex.org/W2084913944","https://openalex.org/W2100263420","https://openalex.org/W2115755118","https://openalex.org/W2116966666","https://openalex.org/W2137146483","https://openalex.org/W2137508792","https://openalex.org/W2156091024","https://openalex.org/W3089488427","https://openalex.org/W3132971798","https://openalex.org/W4246272248","https://openalex.org/W4255272544","https://openalex.org/W4300691479"],"related_works":["https://openalex.org/W2120097785","https://openalex.org/W191391683","https://openalex.org/W3081095613","https://openalex.org/W2144834862","https://openalex.org/W2392326236","https://openalex.org/W2368487145","https://openalex.org/W1985382169","https://openalex.org/W2110834095","https://openalex.org/W2392933489","https://openalex.org/W2036038238"],"abstract_inverted_index":{"The":[0,135,143,156],"theory":[1,25,177],"of":[2,16,29,81,98,121,151,178],"periodic":[3,35],"wavelet":[4,36,102,122,132,154,180],"transforms":[5,123],"presented":[6],"here":[7],"was":[8,185],"originally":[9],"developed":[10,186],"to":[11,66,76,111,165,175],"deal":[12],"with":[13,104,163],"the":[14,24,27,58,92,119,152,176,188],"problem":[15],"epileptic":[17],"seizure":[18,68],"prediction.":[19],"A":[20],"central":[21],"theorem":[22,60],"in":[23,88,140,182],"is":[26,91],"characterization":[28],"wavelets":[30,44,49,128],"having":[31],"time":[32],"and":[33,94,129,191],"scale":[34],"transforms.":[37],"In":[38],"fact,":[39],"we":[40],"prove":[41],"that":[42,57],"such":[43],"are":[45],"precisely":[46],"generalized":[47,100,126],"Haar":[48,101,127],"plus":[50],"a":[51,74,78,99,105,147,160],"logarithmic":[52],"term.":[53],"It":[54],"became":[55],"apparent":[56],"aforementioned":[59],"could":[61,71],"not":[62],"only":[63],"be":[64],"quantified":[65],"analyze":[67],"prediction":[69],"but":[70],"also":[72],"provide":[73],"technique":[75],"address":[77],"large":[79],"class":[80],"periodicity":[82,115,120],"detection":[83,116],"problems.":[84],"An":[85],"essential":[86],"step":[87],"this":[89],"quantification":[90],"geometric":[93],"linear":[95],"algebra":[96],"construction":[97],"associated":[103],"given":[106],"periodicity.":[107],"This":[108,172],"gives":[109],"rise":[110],"an":[112],"algorithm":[113,136,144,162],"for":[114],"based":[117],"on":[118,146],"defined":[124,158],"by":[125,131,187],"implemented":[130],"averaging":[133],"methods.":[134],"detects":[137],"periodicities":[138],"embedded":[139],"significant":[141],"noise.":[142],"depends":[145],"discretized":[148],"version":[149,157],"$W_\\psi^pf(n,m)$":[150,167],"continuous":[153],"transform.":[155],"provides":[159],"fast":[161],"which":[164,184,192],"compute":[166],"from":[168],"$W_\\psi^pf(n-1,m)$":[169],"or":[170],"$W_\\psi^pf(n,m-1)$.":[171],"has":[173],"led":[174],"nondyadic":[179],"frames":[181],"$l^2(\\mathbb{Z})$":[183],"second":[189],"author":[190],"will":[193],"appear":[194],"elsewhere.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
