{"id":"https://openalex.org/W2155441809","doi":"https://doi.org/10.1109/tsp.2009.2020756","title":"Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet Transforms","display_name":"Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet Transforms","publication_year":2009,"publication_date":"2009-04-10","ids":{"openalex":"https://openalex.org/W2155441809","doi":"https://doi.org/10.1109/tsp.2009.2020756","mag":"2155441809"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2020756","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2020756","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":["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/A5046157113","display_name":"\u0130lker Bayram","orcid":"https://orcid.org/0000-0002-4829-5827"},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ilker Bayram","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I90965887","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058321875","display_name":"Ivan Selesnick","orcid":"https://orcid.org/0000-0002-4939-3971"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ivan W. Selesnick","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I90965887","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046157113"],"corresponding_institution_ids":["https://openalex.org/I57206974","https://openalex.org/I90965887"],"apc_list":null,"apc_paid":null,"fwci":7.5457,"has_fulltext":false,"cited_by_count":147,"citation_normalized_percentile":{"value":0.9769728,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"57","issue":"8","first_page":"2957","last_page":"2972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10860","display_name":"Speech and Audio Processing","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7354923486709595},{"id":"https://openalex.org/keywords/emphasis","display_name":"Emphasis (telecommunications)","score":0.6866881251335144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5891811847686768},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.5386736989021301},{"id":"https://openalex.org/keywords/second-generation-wavelet-transform","display_name":"Second-generation wavelet transform","score":0.5228664875030518},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.5035600066184998},{"id":"https://openalex.org/keywords/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.4962993264198303},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4735031723976135},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41929009556770325},{"id":"https://openalex.org/keywords/stationary-wavelet-transform","display_name":"Stationary wavelet transform","score":0.4172285795211792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34722381830215454},{"id":"https://openalex.org/keywords/speech-recognition","display_name":"Speech recognition","score":0.3203203082084656},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21561691164970398},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07260414958000183}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7354923486709595},{"id":"https://openalex.org/C177454536","wikidata":"https://www.wikidata.org/wiki/Q578290","display_name":"Emphasis (telecommunications)","level":2,"score":0.6866881251335144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5891811847686768},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.5386736989021301},{"id":"https://openalex.org/C111350171","wikidata":"https://www.wikidata.org/wiki/Q7443700","display_name":"Second-generation wavelet transform","level":5,"score":0.5228664875030518},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.5035600066184998},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.4962993264198303},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4735031723976135},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41929009556770325},{"id":"https://openalex.org/C73339587","wikidata":"https://www.wikidata.org/wiki/Q1375942","display_name":"Stationary wavelet transform","level":5,"score":0.4172285795211792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34722381830215454},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.3203203082084656},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21561691164970398},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07260414958000183}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2009.2020756","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2020756","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:CiteSeerX.psu:10.1.1.153.3881","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.3881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://taco.poly.edu/selesi/rational/RADWT_2009_preprint.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.3784","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.3784","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://taco.poly.edu/selesi/rational/radwt_fft_2009_preprint.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.722.2362","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.722.2362","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.itu.edu.tr/ibayram/rational.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","display_name":"No poverty","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W17264277","https://openalex.org/W392076736","https://openalex.org/W619413120","https://openalex.org/W1481646516","https://openalex.org/W1512748702","https://openalex.org/W1570190641","https://openalex.org/W1595505223","https://openalex.org/W1610060839","https://openalex.org/W1802935330","https://openalex.org/W1984699259","https://openalex.org/W1985738912","https://openalex.org/W2000406016","https://openalex.org/W2018332268","https://openalex.org/W2019970185","https://openalex.org/W2022394579","https://openalex.org/W2042105302","https://openalex.org/W2062024414","https://openalex.org/W2065675029","https://openalex.org/W2066199162","https://openalex.org/W2067204686","https://openalex.org/W2071039517","https://openalex.org/W2076608692","https://openalex.org/W2096971955","https://openalex.org/W2101689357","https://openalex.org/W2107790757","https://openalex.org/W2107926288","https://openalex.org/W2108862142","https://openalex.org/W2113643684","https://openalex.org/W2119337797","https://openalex.org/W2133528803","https://openalex.org/W2135934764","https://openalex.org/W2143257348","https://openalex.org/W2164697291","https://openalex.org/W2188563164","https://openalex.org/W3151807103","https://openalex.org/W4255272544","https://openalex.org/W4289867895","https://openalex.org/W4292170079"],"related_works":["https://openalex.org/W1986475093","https://openalex.org/W2144408025","https://openalex.org/W2085792030","https://openalex.org/W1588899229","https://openalex.org/W1967182499","https://openalex.org/W1976022598","https://openalex.org/W2205192157","https://openalex.org/W1506615375","https://openalex.org/W1917032666","https://openalex.org/W2391053410"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"The":[3,59,89,139,159],"dyadic":[4,86,103],"wavelet":[5,49,61,87,91,104,130,140,164],"transform":[6,62,92,117,165],"is":[7,93,107],"an":[8,108],"effective":[9],"tool":[10],"for":[11,30,51,72,132],"processing":[12,31,73],"piecewise":[13],"smooth":[14],"signals;":[15],"however,":[16],"its":[17,28],"poor":[18],"frequency":[19,54],"resolution":[20,55],"(its":[21],"low":[22,79],"<emphasis":[23,66,80,133],"emphasistype=\"italic\"><formula":[24,67,81,112,134],"formulatype=\"inline\"><tex":[25,82,135],"Notation=\"TeX\">$Q$</tex></formula></emphasis>-factor)":[26],"limits":[27],"effectiveness":[29],"oscillatory":[32,74],"signals":[33],"like":[34],"speech,":[35],"EEG,":[36],"and":[37,96,123,149,176],"vibration":[38],"measurements,":[39],"etc.":[40],"This":[41],"paper":[42],"develops":[43],"a":[44,129,146],"more":[45],"flexible":[46],"family":[47],"of":[48,84,161,171],"transforms":[50],"which":[52],"the":[53,77,85,102,156,162,168,173,177],"can":[56,63,124,141,150],"be":[57,126,142],"varied.":[58],"new":[60,90,163],"attain":[64],"higher":[65],"formulatype=\"inline\">":[68,113],"<tex":[69,114],"Notation=\"TeX\">$Q$</tex></formula></emphasis>-factors":[70],"(desirable":[71],"signals)":[75],"or":[76],"same":[78],"Notation=\"TeX\">$Q$</tex></formula></emphasis>-factor":[83],"transform.":[88],"modestly":[94],"overcomplete":[95],"based":[97],"on":[98,167],"rational":[99],"dilations.":[100],"Like":[101],"transform,":[105],"it":[106],"easily":[109],"invertible":[110],"'constant-<emphasis":[111],"Notation=\"TeX\">$Q$</tex></formula></emphasis>'":[115],"discrete":[116],"implemented":[118],"using":[119],"iterated":[120],"filter":[121,182],"banks":[122],"likewise":[125],"associated":[127],"with":[128],"frame":[131],"Notation=\"TeX\">$L_{2}(":[136],"{\\BBR":[137],"})$</tex></formula></emphasis>.":[138],"made":[143],"to":[144],"resemble":[145],"Gabor":[147],"function":[148],"hence":[151],"have":[152],"good":[153],"concentration":[154],"in":[155],"time-frequency":[157],"plane.":[158],"construction":[160],"depends":[166],"judicious":[169],"use":[170],"both":[172],"transform's":[174],"redundancy":[175],"flexibility":[178],"allowed":[179],"by":[180],"frequency-domain":[181],"design.":[183],"</para>":[184]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
