{"id":"https://openalex.org/W2055140562","doi":"https://doi.org/10.1109/tsp.2009.2031726","title":"Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes","display_name":"Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes","publication_year":2009,"publication_date":"2009-09-11","ids":{"openalex":"https://openalex.org/W2055140562","doi":"https://doi.org/10.1109/tsp.2009.2031726","mag":"2055140562"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2031726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2031726","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0802.0797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040760837","display_name":"Abdourrahmane M. Atto","orcid":"https://orcid.org/0000-0003-1753-4917"},"institutions":[{"id":"https://openalex.org/I126425946","display_name":"Universit\u00e9 Europ\u00e9enne de Bretagne","ror":"https://ror.org/033c46s90","country_code":"FR","type":"education","lineage":["https://openalex.org/I126425946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A.M. Atto","raw_affiliation_strings":["Institut TELECOM-TELECOM Bretagne,Technop\u00f4le Brest-Iroise, Universit\u00e9 Europ\u00e9enne de Bretagne, Brest, France","SC - D\u00e9partement Signal et Communications (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut TELECOM-TELECOM Bretagne,Technop\u00f4le Brest-Iroise, Universit\u00e9 Europ\u00e9enne de Bretagne, Brest, France","institution_ids":["https://openalex.org/I126425946"]},{"raw_affiliation_string":"SC - D\u00e9partement Signal et Communications (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070406096","display_name":"Dominique Pastor","orcid":"https://orcid.org/0000-0001-5717-5918"},"institutions":[{"id":"https://openalex.org/I126425946","display_name":"Universit\u00e9 Europ\u00e9enne de Bretagne","ror":"https://ror.org/033c46s90","country_code":"FR","type":"education","lineage":["https://openalex.org/I126425946"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210123702","display_name":"Laboratoire des Sciences et Techniques de l\u2019Information de la Communication et de la Connaissance","ror":"https://ror.org/0266kfd37","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I4210123702","https://openalex.org/I4210127572","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4210159245","https://openalex.org/I4405260085"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Pastor","raw_affiliation_strings":["Institut TELECOM-TELECOM Bretagne,Technop\u00f4le Brest-Iroise, Universit\u00e9 Europ\u00e9enne de Bretagne, Brest, France","Lab-STICC_TB_CID_TOMS (France)","SC - D\u00e9partement Signal et Communications (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut TELECOM-TELECOM Bretagne,Technop\u00f4le Brest-Iroise, Universit\u00e9 Europ\u00e9enne de Bretagne, Brest, France","institution_ids":["https://openalex.org/I126425946"]},{"raw_affiliation_string":"Lab-STICC_TB_CID_TOMS (France)","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I4210123702"]},{"raw_affiliation_string":"SC - D\u00e9partement Signal et Communications (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9356,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87636035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"2","first_page":"896","last_page":"901"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.987500011920929,"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":0.9674000144004822,"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/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.6862883567810059},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6724955439567566},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6483689546585083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6346806287765503},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4684869050979614},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.4663502275943756},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4586179256439209},{"id":"https://openalex.org/keywords/network-packet","display_name":"Network packet","score":0.4537392854690552},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.44852983951568604},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.44516322016716003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.416401207447052},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3907548189163208},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34004586935043335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32511216402053833},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2936598062515259},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.2851617932319641},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.276987224817276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27157682180404663},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2188299000263214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11374098062515259},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11194431781768799},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06894677877426147}],"concepts":[{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.6862883567810059},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6724955439567566},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6483689546585083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6346806287765503},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4684869050979614},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.4663502275943756},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4586179256439209},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.4537392854690552},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.44852983951568604},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.44516322016716003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.416401207447052},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3907548189163208},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34004586935043335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32511216402053833},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2936598062515259},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.2851617932319641},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.276987224817276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27157682180404663},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2188299000263214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11374098062515259},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11194431781768799},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06894677877426147},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tsp.2009.2031726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2031726","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0802.0797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0802.0797","pdf_url":"https://arxiv.org/pdf/0802.0797","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.242.8851","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.242.8851","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.0797v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.2431","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.2431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.0797v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.426","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.426","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.0797v2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00241849v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00241849","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, 2009, 58 (2), pp.896-901. ⟨10.1109/TSP.2009.2031726⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0802.0797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0802.0797","pdf_url":"https://arxiv.org/pdf/0802.0797","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1595505223","https://openalex.org/W1663998522","https://openalex.org/W1665018376","https://openalex.org/W2032268516","https://openalex.org/W2040688149","https://openalex.org/W2055065194","https://openalex.org/W2062024414","https://openalex.org/W2097656822","https://openalex.org/W2109442086","https://openalex.org/W2115755118","https://openalex.org/W2116049366","https://openalex.org/W2137440839","https://openalex.org/W2156899486","https://openalex.org/W2158940042","https://openalex.org/W2160627537","https://openalex.org/W2160846724","https://openalex.org/W3103104196","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W1520848345","https://openalex.org/W2536361827","https://openalex.org/W631963756","https://openalex.org/W2389176696","https://openalex.org/W1997959843","https://openalex.org/W2371424935","https://openalex.org/W2155098316","https://openalex.org/W3103996772","https://openalex.org/W2365691107","https://openalex.org/W2478197576"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"central":[3],"limit":[4,87],"theorems":[5],"for":[6,21],"the":[7,22,25,31,48,64,70,83,86,94,97],"wavelet":[8,26,39],"packet":[9,27,40],"decomposition":[10,41,71],"of":[11,24,33,37,77,85,96],"stationary":[12],"band-limited":[13],"random":[14],"processes.":[15],"The":[16],"asymptotic":[17],"analysis":[18],"is":[19,44,51],"performed":[20],"sequences":[23,55],"coefficients":[28],"returned":[29],"at":[30,103],"nodes":[32],"any":[34,80],"given":[35,81],"path":[36],"theM-band":[38],"tree.":[42],"It":[43],"shown":[45],"that":[46,69],"if":[47],"input":[49,98],"process":[50,90,99],"strictly":[52],"stationary,":[53],"these":[54],"converge":[56],"in":[57],"distribution":[58],"to":[59,93],"white":[60,88],"Gaussian":[61,89],"processes":[62],"when":[63],"resolution":[65],"level":[66],"increases,":[67],"provided":[68],"filters":[72],"satisfy":[73],"a":[74,104],"suitable":[75],"property":[76],"regularity.":[78],"For":[79],"path,":[82],"variance":[84],"directly":[91],"relates":[92],"value":[95],"power":[100],"spectral":[101],"density":[102],"specific":[105],"frequency.":[106]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}