{"id":"https://openalex.org/W2018288743","doi":"https://doi.org/10.1109/lsp.2015.2402395","title":"Multichannel Random Discrete Fractional Fourier Transform","display_name":"Multichannel Random Discrete Fractional Fourier Transform","publication_year":2015,"publication_date":"2015-02-10","ids":{"openalex":"https://openalex.org/W2018288743","doi":"https://doi.org/10.1109/lsp.2015.2402395","mag":"2018288743"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2402395","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2402395","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/7017605/07038207.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ieeexplore.ieee.org/ielx7/97/7017605/07038207.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083632340","display_name":"Xuejing Kang","orcid":"https://orcid.org/0000-0002-4088-351X"},"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":"Xuejing Kang","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100784476","display_name":"Feng Zhang","orcid":"https://orcid.org/0000-0003-2643-6446"},"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":"Feng Zhang","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","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":false,"raw_author_name":"Ran Tao","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":6.2037,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.96539919,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"9","first_page":"1340","last_page":"1344"},"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":0.9939000010490417,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9908999800682068,"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":0.6857308149337769},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6602690815925598},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5660915970802307},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5653097629547119},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.554699182510376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5454621315002441},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5166962146759033},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.42611682415008545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39310309290885925},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.36184293031692505},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.344347208738327},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.21753111481666565},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1772189438343048},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16945070028305054},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08986315131187439}],"concepts":[{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.6857308149337769},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6602690815925598},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5660915970802307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5653097629547119},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.554699182510376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5454621315002441},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5166962146759033},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.42611682415008545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39310309290885925},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.36184293031692505},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.344347208738327},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.21753111481666565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1772189438343048},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16945070028305054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08986315131187439},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2015.2402395","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2402395","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/7017605/07038207.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/lsp.2015.2402395","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2402395","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/7017605/07038207.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4639895821","display_name":null,"funder_award_id":"61421001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6952756739","display_name":null,"funder_award_id":"61331021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8150318114","display_name":null,"funder_award_id":"61201354","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G952708899","display_name":null,"funder_award_id":"YETP1221","funder_id":"https://openalex.org/F4320335442","funder_display_name":"Beijing Higher Education Young Elite Teacher Project"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335442","display_name":"Beijing Higher Education Young Elite Teacher Project","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018288743.pdf","grobid_xml":"https://content.openalex.org/works/W2018288743.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W606473257","https://openalex.org/W1981898695","https://openalex.org/W2008541946","https://openalex.org/W2025328969","https://openalex.org/W2028023382","https://openalex.org/W2035195608","https://openalex.org/W2057875231","https://openalex.org/W2062380581","https://openalex.org/W2063499859","https://openalex.org/W2072370646","https://openalex.org/W2082685661","https://openalex.org/W2085220963","https://openalex.org/W2092968959","https://openalex.org/W2101778459","https://openalex.org/W2110063971","https://openalex.org/W2146267335","https://openalex.org/W2149720531","https://openalex.org/W2169175428","https://openalex.org/W2183889480"],"related_works":["https://openalex.org/W2118155316","https://openalex.org/W2382218334","https://openalex.org/W2090697566","https://openalex.org/W2362643922","https://openalex.org/W2116983948","https://openalex.org/W2155549970","https://openalex.org/W3141389362","https://openalex.org/W2057875231","https://openalex.org/W2140256262","https://openalex.org/W2183119314"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,35,41,102],"multichannel":[3],"random":[4,11,44],"discrete":[5],"fractional":[6],"Fourier":[7],"transform":[8,16],"(MRFrFT)":[9],"with":[10],"weighting":[12,21],"coefficients":[13,22],"and":[14,57,59,63,84,114],"partial":[15],"kernel":[17,30],"functions.":[18],"First,":[19],"the":[20,29,75,82,93,110,115,118],"of":[23,43,86,95],"each":[24],"channel":[25],"are":[26,38,89],"randomized.":[27],"Then,":[28],"functions,":[31],"selected":[32],"based":[33],"on":[34],"choice":[36],"scheme,":[37],"randomized":[39],"using":[40],"group":[42],"phase-only":[45],"masks":[46],"(RPOMs).":[47],"The":[48],"proposed":[49],"MRFrFT":[50,76,94],"can":[51,98],"be":[52,99],"carried":[53],"out":[54],"both":[55,90],"electronically":[56],"optically,":[58],"its":[60,87],"main":[61],"features":[62],"properties":[64],"have":[65],"been":[66],"given.":[67],"Numerical":[68],"simulation":[69],"about":[70],"one-dimensional":[71],"signal":[72],"demonstrates":[73],"that":[74,81],"has":[77],"an":[78],"important":[79],"feature":[80],"magnitude":[83],"phase":[85],"output":[88],"random.":[91],"Moreover,":[92],"two-dimensional":[96],"image":[97,105],"viewed":[100],"as":[101],"security":[103],"enhanced":[104],"encryption":[106],"scheme":[107],"due":[108],"to":[109,117],"large":[111],"key":[112],"space":[113],"sensitivity":[116],"private":[119],"keys.":[120]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}