{"id":"https://openalex.org/W1967489373","doi":"https://doi.org/10.1109/tsp.2010.2089680","title":"Transform Order Division Multiplexing","display_name":"Transform Order Division Multiplexing","publication_year":2010,"publication_date":"2010-11-05","ids":{"openalex":"https://openalex.org/W1967489373","doi":"https://doi.org/10.1109/tsp.2010.2089680","mag":"1967489373"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2010.2089680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2089680","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/A5067803447","display_name":"Ran Tao","orcid":"https://orcid.org/0000-0002-5243-7189"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ran Tao","raw_affiliation_strings":["Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100853838","display_name":"Xiang-Yi Meng","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang-Yi Meng","raw_affiliation_strings":["Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100371964","display_name":"Yue Wang","orcid":"https://orcid.org/0000-0001-7356-5991"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Wang","raw_affiliation_strings":["Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Beijing Inst. of Technol., Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067803447"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":2.4371,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86592296,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"59","issue":"2","first_page":"598","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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":0.9998999834060669,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9939000010490417,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9869999885559082,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.8012911081314087},{"id":"https://openalex.org/keywords/multiplexing","display_name":"Multiplexing","score":0.6922997236251831},{"id":"https://openalex.org/keywords/orthogonal-frequency-division-multiplexing","display_name":"Orthogonal frequency-division multiplexing","score":0.5858302116394043},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.561104416847229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5208514332771301},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5204529762268066},{"id":"https://openalex.org/keywords/frequency-division-multiplexing","display_name":"Frequency-division multiplexing","score":0.5088903903961182},{"id":"https://openalex.org/keywords/time-division-multiplexing","display_name":"Time-division multiplexing","score":0.4944629669189453},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46142226457595825},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.45740535855293274},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.42907702922821045},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.4186145067214966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33291226625442505},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.3230532109737396},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.19973021745681763},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.13971391320228577},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10058745741844177},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08631962537765503}],"concepts":[{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.8012911081314087},{"id":"https://openalex.org/C19275194","wikidata":"https://www.wikidata.org/wiki/Q222903","display_name":"Multiplexing","level":2,"score":0.6922997236251831},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.5858302116394043},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.561104416847229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5208514332771301},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5204529762268066},{"id":"https://openalex.org/C89061704","wikidata":"https://www.wikidata.org/wiki/Q5555726","display_name":"Frequency-division multiplexing","level":4,"score":0.5088903903961182},{"id":"https://openalex.org/C50661577","wikidata":"https://www.wikidata.org/wiki/Q901831","display_name":"Time-division multiplexing","level":3,"score":0.4944629669189453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46142226457595825},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.45740535855293274},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.42907702922821045},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.4186145067214966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33291226625442505},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.3230532109737396},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.19973021745681763},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.13971391320228577},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10058745741844177},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08631962537765503},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2010.2089680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2089680","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1554624397","https://openalex.org/W1568450818","https://openalex.org/W1970914944","https://openalex.org/W1974911306","https://openalex.org/W2018654957","https://openalex.org/W2031720721","https://openalex.org/W2075511533","https://openalex.org/W2082819064","https://openalex.org/W2100619198","https://openalex.org/W2100912680","https://openalex.org/W2101441465","https://openalex.org/W2106416113","https://openalex.org/W2108710836","https://openalex.org/W2110063971","https://openalex.org/W2116983948","https://openalex.org/W2117472877","https://openalex.org/W2120230078","https://openalex.org/W2121185552","https://openalex.org/W2124300121","https://openalex.org/W2127769464","https://openalex.org/W2136106070","https://openalex.org/W2145576488","https://openalex.org/W2145682890","https://openalex.org/W2157006006","https://openalex.org/W2166169870","https://openalex.org/W2169103119","https://openalex.org/W2169175428","https://openalex.org/W2169773841","https://openalex.org/W2475405239"],"related_works":["https://openalex.org/W2118155316","https://openalex.org/W2382218334","https://openalex.org/W4226230195","https://openalex.org/W1998182654","https://openalex.org/W2003701703","https://openalex.org/W2092309091","https://openalex.org/W43516829","https://openalex.org/W1594984840","https://openalex.org/W2009574894","https://openalex.org/W2284861921"],"abstract_inverted_index":{"Multiplexing":[0],"in":[1,11,15,42,58,61,128],"the":[2,9,16,20,24,38,43,47,55,59,62,78,81,85,88,91,95,98,106,113,116,119,122,126,129,131,137,140,149],"fractional":[3,25],"Fourier":[4,26],"domain":[5],"(FRFD)":[6],"only":[7],"transmits":[8,54],"signals":[10],"a":[12],"single":[13],"direction":[14],"time-frequency":[17,63],"plane":[18,64],"and":[19,97,121,136],"transform":[21,27,48],"order":[22,49],"of":[23,80,90,105,139],"(FRFT)":[28],"is":[29,109,133,142],"not":[30],"used":[31],"sufficiently.":[32],"In":[33],"this":[34],"paper,":[35],"we":[36],"apply":[37],"perfect":[39],"reconstruction":[40,117],"transmultiplexer":[41],"FRFD":[44],"to":[45],"develop":[46],"division":[50],"multiplexing":[51,127],"(TODM),":[52],"which":[53],"original":[56,82,92],"information":[57,83,93],"multidirections":[60],"simultaneously.":[65],"The":[66,102],"proposed":[67],"TODM":[68,107,132],"systems":[69,108],"can":[70],"be":[71],"divided":[72],"into":[73],"two":[74],"types.":[75],"One":[76],"needs":[77,87],"multitransmission":[79],"while":[84],"other":[86],"modifications":[89],"by":[94],"interpolation":[96],"inverse":[99],"discrete":[100],"FRFT.":[101],"performance":[103],"analysis":[104],"also":[110],"presented,":[111],"including":[112],"system":[114,141],"capacity,":[115],"accuracy,":[118],"security,":[120],"limitation.":[123],"Compared":[124],"with":[125],"FRFD,":[130],"more":[134],"flexible":[135],"security":[138],"highly":[143],"strengthened.":[144],"Finally,":[145],"simulation":[146],"results":[147],"confirm":[148],"obtained":[150],"analytical":[151],"results.":[152]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}