{"id":"https://openalex.org/W2166705561","doi":"https://doi.org/10.1109/ccece.2009.5090192","title":"Novel nearly tridiagonal commuting matrix and fractionalizations of generalized DFT matrix","display_name":"Novel nearly tridiagonal commuting matrix and fractionalizations of generalized DFT matrix","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2166705561","doi":"https://doi.org/10.1109/ccece.2009.5090192","mag":"2166705561"},"language":"en","primary_location":{"id":"doi:10.1109/ccece.2009.5090192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccece.2009.5090192","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 Canadian Conference on Electrical and Computer Engineering","raw_type":"proceedings-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":null,"display_name":"Qi-Wen Ran","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi-Wen Ran","raw_affiliation_strings":["Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063959796","display_name":"Zhongzhao Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong-Zhao Zhang","raw_affiliation_strings":["Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067794103","display_name":"Deyun Wei","orcid":"https://orcid.org/0000-0003-0181-9264"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"De-Yun Wei","raw_affiliation_strings":["Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083179738","display_name":"Xuejun Sha","orcid":"https://orcid.org/0000-0002-6204-0839"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xue-Jun Sha","raw_affiliation_strings":["Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20352975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"555","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9965999722480774,"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":0.9854999780654907,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7475129961967468},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.7125338315963745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.647003173828125},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.5723355412483215},{"id":"https://openalex.org/keywords/dft-matrix","display_name":"DFT matrix","score":0.5406498312950134},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.5005040168762207},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4789983928203583},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4456355571746826},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.43477416038513184},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43202900886535645},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.4214288294315338},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4093686044216156},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.24050673842430115},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.22397685050964355},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12881851196289062},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.09585171937942505},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.0663112998008728}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7475129961967468},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.7125338315963745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.647003173828125},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.5723355412483215},{"id":"https://openalex.org/C103945485","wikidata":"https://www.wikidata.org/wiki/Q5204933","display_name":"DFT matrix","level":5,"score":0.5406498312950134},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.5005040168762207},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4789983928203583},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4456355571746826},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.43477416038513184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43202900886535645},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.4214288294315338},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4093686044216156},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.24050673842430115},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.22397685050964355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12881851196289062},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.09585171937942505},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0663112998008728},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ccece.2009.5090192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccece.2009.5090192","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 Canadian Conference on Electrical and Computer Engineering","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W606473257","https://openalex.org/W1993720318","https://openalex.org/W2013737143","https://openalex.org/W2075735090","https://openalex.org/W2082685661","https://openalex.org/W2090697566","https://openalex.org/W2116983948","https://openalex.org/W2132538465","https://openalex.org/W2149510369","https://openalex.org/W2170713639","https://openalex.org/W3022136271"],"related_works":["https://openalex.org/W2945379152","https://openalex.org/W2118155316","https://openalex.org/W2128992369","https://openalex.org/W2343504300","https://openalex.org/W2142891205","https://openalex.org/W1978432871","https://openalex.org/W2356259437","https://openalex.org/W2090697566","https://openalex.org/W2963406743","https://openalex.org/W2146267335"],"abstract_inverted_index":{"Based":[0],"on":[1,60],"discrete":[2,6,41],"Hermite-Gaussian-like":[3],"functions,":[4],"a":[5,31,54],"fractional":[7,18,95,120],"Fourier":[8,19,42,121],"transform":[9,43,96,111,122],"(DFRFT),":[10],"which":[11,36,81],"provides":[12],"sample":[13],"approximations":[14],"of":[15,63,69,97,107,117],"the":[16,39,70,86,115,118],"continuous":[17,87,119],"transform,":[20],"was":[21],"defined":[22,101],"and":[23],"investigated":[24],"recently.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29],"propose":[30],"novel":[32],"nearly":[33,72],"tridiagonal":[34,73],"matrix,":[35],"commutes":[37],"with":[38],"generalized":[40],"(GDFT)":[44],"matrix.":[45,66],"It":[46],"doesn't":[47],"has":[48],"repeated":[49],"eigenvalue.":[50],"We":[51],"can":[52],"determine":[53],"unique":[55],"orthonormal":[56],"eigenvector":[57],"set":[58],"based":[59],"block":[61],"diagonalization":[62],"new":[64,71,105],"commuting":[65],"The":[67,94,104],"eigenvectors":[68],"matrix":[74],"are":[75,82],"shown":[76],"to":[77,85,114],"be":[78],"GDFT":[79,98],"eigenvectors,":[80],"more":[83],"similar":[84],"Hermite-Gaussian":[88],"functions":[89],"than":[90],"those":[91],"developed":[92],"before.":[93],"(GDFRFT)":[99],"is":[100],"through":[102,123],"eigendecomposition.":[103],"version":[106],"GDFRFT":[108],"produce":[109],"their":[110],"outputs":[112],"closer":[113],"samples":[116],"numerical":[124],"comparison.":[125]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}