On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly...

Full description

Saved in:
Bibliographic Details
Published in:Electronics (Basel) Vol. 10; no. 9; p. 1117
Main Authors: Li, Bin, Jiang, Zhikang, Chen, Jie
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2021
Subjects:
Algorithms
Aliasing
Computation
Experiments
Fast Fourier transformations
Fourier transforms
Graph theory
Iterative methods
Magnetic resonance imaging
Performance evaluation
Run time (computers)
ISSN:2079-9292, 2079-9292
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.
AbstractList Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.
Author Li, Bin
Jiang, Zhikang
Chen, Jie
Author_xml – sequence: 1
  givenname: Bin
  surname: Li
  fullname: Li, Bin
– sequence: 2
  givenname: Zhikang
  orcidid: 0000-0002-6213-3357
  surname: Jiang
  fullname: Jiang, Zhikang
– sequence: 3
  givenname: Jie
  surname: Chen
  fullname: Chen, Jie
BookMark eNp9kE9LAzEQxYNUsNZ-Ai8Bz6v5s9skx1JcFQoVbM_LdHe2TdkmNUkPfnu31oOIeJqZx-_NDO-aDJx3SMgtZ_dSGvaAHdYpeGfryBkznHN1QYaCKZMZYcTgR39FxjHuGDthUks2JMuFo68YWh_24GqkvqVvBwgRaQkx0dIfg8VAlwFcPEF02m18sGm7j3QVrdvQtMVetPA1lLZLGG7IZQtdxPF3HZFV-bicPWfzxdPLbDrPailEypTU0ExaptSkzdeNFKA4Ry3FGhGgQQ4TZnodddMI06p13uTAUekiRwW1liNyd957CP79iDFVu_5f15-sRCG0KLTgRU_JM1UHH2PAtjoEu4fwUXFWnRKs_kiwd5lfrtomSNa7FMB2_3o_AaEpfV4
CitedBy_id crossref_primary_10_1109_JSEN_2023_3268295
crossref_primary_10_1109_JSEN_2024_3370234
crossref_primary_10_3390_electronics11152291
crossref_primary_10_1007_s00034_022_01989_6
crossref_primary_10_23919_JSEE_2024_000015
crossref_primary_10_3390_s21237808
crossref_primary_10_1109_ACCESS_2021_3095071
Cites_doi 10.1137/1.9781611973099.93
10.1109/FOCS.2017.66
10.1137/1.9781611975482.168
10.1109/ISIT.2013.6620269
10.1109/ACCESS.2020.2989327
10.1109/IPDPS.2016.95
10.1109/TSP.2018.2878546
10.1109/29.45547
10.1016/j.acha.2015.04.002
10.1007/s00041-018-9616-4
10.1109/ICASSP.2013.6638743
10.1109/TIT.2017.2746568
10.1137/1.9781611973402.36
10.1007/s11075-017-0370-5
10.1109/ISSCC.2014.6757512
10.1007/s10208-009-9057-1
10.1142/S1793536913500039
10.1109/TSP.2017.2740198
10.4310/CMS.2007.v5.n4.a13
10.1109/ACCESS.2018.2853180
10.1109/TIT.1964.1053699
10.1016/j.acha.2012.03.007
10.1016/j.cam.2017.03.019
10.1145/2213977.2214029
10.1109/ICASSP.2019.8682063
10.1016/0377-0427(88)90386-X
10.1109/MSP.2014.2329131
10.1090/S0025-5718-1965-0178586-1
10.1109/29.56027
10.1109/SiPS.2014.6986055
10.1109/MSP.2007.915000
10.1007/s00034-019-01136-8
10.1007/s11075-015-0028-0
10.17230/ingciencia.11.22.4
ContentType Journal Article
Copyright 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
7SP
8FD
8FE
8FG
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L7M
P5Z
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
DOI 10.3390/electronics10091117
DatabaseName CrossRef
Electronics & Communications Abstracts
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
ProQuest Technology Collection
ProQuest One
ProQuest Central Korea
SciTech Premium Collection
Advanced Technologies Database with Aerospace
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
Proquest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
DatabaseTitle CrossRef
Publicly Available Content Database
Advanced Technologies & Aerospace Collection
Technology Collection
Technology Research Database
ProQuest One Academic Middle East (New)
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
Electronics & Communications Abstracts
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central
Advanced Technologies & Aerospace Database
ProQuest One Applied & Life Sciences
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
Advanced Technologies Database with Aerospace
ProQuest One Academic (New)
DatabaseTitleList CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: ProQuest Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2079-9292
ExternalDocumentID 10_3390_electronics10091117
GroupedDBID 5VS
8FE
8FG
AAYXX
ADMLS
AFFHD
AFKRA
ALMA_UNASSIGNED_HOLDINGS
ARAPS
BENPR
BGLVJ
CCPQU
CITATION
HCIFZ
IAO
KQ8
MODMG
M~E
OK1
P62
PHGZM
PHGZT
PIMPY
PQGLB
PROAC
7SP
8FD
ABUWG
AZQEC
DWQXO
L7M
PKEHL
PQEST
PQQKQ
PQUKI
ID FETCH-LOGICAL-c322t-738ad6f0776f4bd32a711e832beeaade1a609bd3e8dd29f7b4d4a1e7854e7ac83
IEDL.DBID P5Z
ISICitedReferencesCount 9
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000649987100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2079-9292
IngestDate Sun Nov 09 06:07:13 EST 2025
Sat Nov 29 07:14:30 EST 2025
Tue Nov 18 22:24:36 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 9
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c322t-738ad6f0776f4bd32a711e832beeaade1a609bd3e8dd29f7b4d4a1e7854e7ac83
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-6213-3357
OpenAccessLink https://www.proquest.com/docview/2528258215?pq-origsite=%requestingapplication%
PQID 2528258215
PQPubID 2032404
ParticipantIDs proquest_journals_2528258215
crossref_primary_10_3390_electronics10091117
crossref_citationtrail_10_3390_electronics10091117
PublicationCentury 2000
PublicationDate 2021-05-01
PublicationDateYYYYMMDD 2021-05-01
PublicationDate_xml – month: 05
  year: 2021
  text: 2021-05-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Electronics (Basel)
PublicationYear 2021
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Iwen (ref_16) 2010; 10
Plonka (ref_33) 2016; 71
Li (ref_8) 2020; 8
Plonka (ref_34) 2017; 321
ref_14
ref_36
ref_13
Chien (ref_35) 1964; 10
ref_11
ref_10
Christlieb (ref_19) 2016; 40
ref_30
Cooley (ref_1) 1965; 19
ref_18
ref_15
ref_37
Iwen (ref_17) 2013; 34
Chen (ref_25) 2017; 65
Wang (ref_29) 2019; 67
Kay (ref_38) 1989; 37
Gilbert (ref_4) 2008; 25
Gilbert (ref_21) 2014; 31
Gilbert (ref_2) 2002; 2
ref_23
Kumar (ref_32) 2019; 38
ref_22
Iwen (ref_3) 2007; 5
Merhi (ref_20) 2019; 25
Pang (ref_31) 2018; 6
ref_28
ref_27
ref_26
ref_9
Pawar (ref_12) 2018; 64
(ref_24) 2015; 11
ref_5
ref_7
ref_6
References_xml – ident: ref_7
– ident: ref_5
  doi: 10.1137/1.9781611973099.93
– ident: ref_22
  doi: 10.1109/FOCS.2017.66
– ident: ref_30
  doi: 10.1137/1.9781611975482.168
– ident: ref_11
  doi: 10.1109/ISIT.2013.6620269
– volume: 8
  start-page: 79134
  year: 2020
  ident: ref_8
  article-title: On performance of sparse fast Fourier transform algorithms using the flat window filter
  publication-title: IEEE Access
  doi: 10.1109/ACCESS.2020.2989327
– ident: ref_27
  doi: 10.1109/IPDPS.2016.95
– volume: 67
  start-page: 54
  year: 2019
  ident: ref_29
  article-title: Multidimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2018.2878546
– volume: 37
  start-page: 1987
  year: 1989
  ident: ref_38
  article-title: A Fast and Accurate Single Frequency Estimator
  publication-title: IEEE Trans. Acoust. Speech Signal Process.
  doi: 10.1109/29.45547
– volume: 40
  start-page: 553
  year: 2016
  ident: ref_19
  article-title: A multiscale sub-linear time Fourier algorithm for noisy data
  publication-title: Appl. Comput. Harmon. Anal.
  doi: 10.1016/j.acha.2015.04.002
– volume: 25
  start-page: 751
  year: 2019
  ident: ref_20
  article-title: A New Class of Fully Discrete Sparse Fourier Transforms: Faster Stable Implementations with Guarantees
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/s00041-018-9616-4
– ident: ref_9
  doi: 10.1109/ICASSP.2013.6638743
– volume: 64
  start-page: 429
  year: 2018
  ident: ref_12
  article-title: FFAST: An algorithm for computing an exactly k-Sparse DFT in O(k log k) time
  publication-title: IEEE Trans. Inf. Theory
  doi: 10.1109/TIT.2017.2746568
– ident: ref_23
  doi: 10.1137/1.9781611973402.36
– ident: ref_15
  doi: 10.1007/s11075-017-0370-5
– ident: ref_28
  doi: 10.1109/ISSCC.2014.6757512
– volume: 10
  start-page: 303
  year: 2010
  ident: ref_16
  article-title: Combinatorial sublinear-time Fourier algorithms
  publication-title: Found. Comput. Math.
  doi: 10.1007/s10208-009-9057-1
– ident: ref_18
  doi: 10.1142/S1793536913500039
– volume: 65
  start-page: 5716
  year: 2017
  ident: ref_25
  article-title: On Performance of Sparse Fast Fourier Transform and Enhancement Algorithm
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2017.2740198
– volume: 5
  start-page: 981
  year: 2007
  ident: ref_3
  article-title: Empirical evaluation of a sub-linear time sparse DFT algorithm
  publication-title: Commun. Math. Sci.
  doi: 10.4310/CMS.2007.v5.n4.a13
– volume: 6
  start-page: 37828
  year: 2018
  ident: ref_31
  article-title: High-speed target detection algorithm based on sparse Fourier transform
  publication-title: IEEE Access
  doi: 10.1109/ACCESS.2018.2853180
– volume: 10
  start-page: 357
  year: 1964
  ident: ref_35
  article-title: Cyclic Decoding Procedures for Bose-Chaudhuri-Hocquenghem Codes
  publication-title: IEEE Trans. Inf. Theory
  doi: 10.1109/TIT.1964.1053699
– ident: ref_10
– volume: 34
  start-page: 57
  year: 2013
  ident: ref_17
  article-title: Improved approximation guarantees for sublinear-time Fourier algorithms
  publication-title: Appl. Comput. Harmon. Anal.
  doi: 10.1016/j.acha.2012.03.007
– volume: 321
  start-page: 532
  year: 2017
  ident: ref_34
  article-title: A sparse fast Fourier algorithm for real non-negative vectors
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2017.03.019
– ident: ref_6
  doi: 10.1145/2213977.2214029
– ident: ref_14
  doi: 10.1109/ICASSP.2019.8682063
– ident: ref_36
  doi: 10.1016/0377-0427(88)90386-X
– ident: ref_13
– volume: 31
  start-page: 91
  year: 2014
  ident: ref_21
  article-title: Recent Developments in the Sparse Fourier Transform
  publication-title: Signal Processing Mag.
  doi: 10.1109/MSP.2014.2329131
– volume: 19
  start-page: 297
  year: 1965
  ident: ref_1
  article-title: An Algorithm for the Machine Calculation of Complex Fourier Series
  publication-title: Math. Comput.
  doi: 10.1090/S0025-5718-1965-0178586-1
– ident: ref_37
  doi: 10.1109/29.56027
– ident: ref_26
  doi: 10.1109/SiPS.2014.6986055
– volume: 2
  start-page: 152
  year: 2002
  ident: ref_2
  article-title: Near-optimal sparse Fourier representations via sampling
  publication-title: Conf. Proc. Annu. ACM Symp. Theory Comput.
– volume: 25
  start-page: 57
  year: 2008
  ident: ref_4
  article-title: A tutorial on fast Fourier sampling: How to apply it to problems
  publication-title: IEEE Signal Process. Mag.
  doi: 10.1109/MSP.2007.915000
– volume: 38
  start-page: 5665
  year: 2019
  ident: ref_32
  article-title: 50 Years of FFT Algorithms and Applications
  publication-title: Circuits Syst. Signal Process.
  doi: 10.1007/s00034-019-01136-8
– volume: 71
  start-page: 889
  year: 2016
  ident: ref_33
  article-title: A deterministic sparse FFT algorithm for vectors with small support
  publication-title: Numer. Algorithms
  doi: 10.1007/s11075-015-0028-0
– volume: 11
  start-page: 73
  year: 2015
  ident: ref_24
  article-title: Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case
  publication-title: Ingeniería y Ciencia
  doi: 10.17230/ingciencia.11.22.4
SSID ssj0000913830
Score 2.2400155
Snippet Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More...
SourceID proquest
crossref
SourceType Aggregation Database
Enrichment Source
Index Database
StartPage 1117
SubjectTerms Algorithms
Aliasing
Computation
Experiments
Fast Fourier transformations
Fourier transforms
Graph theory
Iterative methods
Magnetic resonance imaging
Performance evaluation
Run time (computers)
Title On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter
URI https://www.proquest.com/docview/2528258215
Volume 10
WOSCitedRecordID wos000649987100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2079-9292
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913830
  issn: 2079-9292
  databaseCode: M~E
  dateStart: 20120101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Advanced Technologies & Aerospace Database
  customDbUrl:
  eissn: 2079-9292
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913830
  issn: 2079-9292
  databaseCode: P5Z
  dateStart: 20120301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2079-9292
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913830
  issn: 2079-9292
  databaseCode: BENPR
  dateStart: 20120301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Publicly Available Content Database
  customDbUrl:
  eissn: 2079-9292
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913830
  issn: 2079-9292
  databaseCode: PIMPY
  dateStart: 20120301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED5BYYCBN6JQKg-MRDSx0zgTKqgRDJQIigQskeMHVCppaQIjv51zmlKQEAtjbEeJfL6Xff4-gCNBjQiZzx3hUkxQjGk7qadTx5OYxikvTJmQJdlE0Ovx-_swrjbc8qqscmYTS0OtRtLukZ94vr1lydFDnY5fHcsaZU9XKwqNRViyKAmWuiH2H7_2WCzmJaetKdgQxez-ZM4tk7u22y2Jyr45pJ_2uHQy0fp_f28D1qrwknSm62ETFnS2BavfQAe3oX-dkXh-XYCMDLkdY3qrSSTygkRTEjvSn0W0pDN8wi8Vzy85KQsMCMaM2DgQ5UM0sOftO3AXdfvnF07FreBIVOHCCSgXqm0smI9hqaKeCFxXo3qnWguhtCvarRDbNVcoMROkTDHh6oD7TAdCcroLtWyU6T0gqMEtHuhQSsaYojx1lcHBPg19g9GmqIM3m-BEVsDjlv9imGACYqWS_CKVOhx_vTSe4m78PbwxE0tSKWGezGWy_3f3Aax4tlSlrGNsQK2YvOlDWJbvxSCfNGHprNuLb5qwePXRbZYrDNviy6v44RN-Ot5z
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LTtwwFL2CoRJ0AZSHyqt40e6ImNjOxFkghICIETAdqYMEq-D4ASPRmSkJIH6Kb-Q6DwYkxI5Fl7GdKI6P7sO5Pgfgp2RWRjwQnvQZJijWtryUmtSjCtM4TaOUS1WITYSdjjg_j7oT8FSfhXFllbVNLAy1Hiq3R75NA3fKUqCH2h3985xqlPu7WktolLA4No8PmLJlO-0DXN9flMaHvf0jr1IV8BSCN_dCJqRuWUdjY3mqGZWh7xsEdmqMlNr4stWMsN0Ije9qw5RrLn0TioCbUCrB8LmTMMUd2Bsw1W2fdi9ednUcy6ZgzZLeiLGouT1Ws8l81-0X0mivXOBbD1C4tXjuf_sg8zBbBdBkr0T8N5gwgwX4-opWcRF6vwekOz4QQYaW_BlhAm9ILLOcxKVMH-nVMTvZu7nCmeXXfzNSlFAQjIqxsS-Li7jvKgqW4OxTprUMjcFwYL4DQRvVFKGJlOKcayZSX1scHLAosBhPyxWg9YImqqJWdwofNwmmWA4FyTsoWIGtl5tGJbPIx8PXaxgklZnJkjEGVj_u3oTpo97pSXLS7hyvwQx1hTlF1eY6NPLbO7MBX9R93s9uf1SIJnD52Zh5BrbTOuI
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LTuMwFL1iAI1gwWMGxBsvYDdRG9tpnAVCCIhAoFKJjoRmk3H8gErQFhJA_Bpfx3UeFCTEjgXLOE4Uxyf34RzfA7AlmZURD4QnfYYJirUtL6Um9ajCNE7TKOVSFWITYbstLi6izhg813thHK2ytomFodYD5dbIGzRwuywFeqiGrWgRnYN4d3jrOQUp96e1ltMoIXJinh4xfct2jg9wrrcpjQ-7-0depTDgKQRy7oVMSN2yrqSN5almVIa-bxDkqTFSauPLVjPCdiM0PrcNU6659E0oAm5CqQTD-_6AiRBzTEcn7AT_Xtd3XL1NwZploSPGomZjpGuT-e60X4ikvXGG731B4eDi2e_8auZgpgqryV75HczDmOn_guk3xRZ_Q_esTzqjbRJkYMn5ENN6Q2KZ5SQuxftIt47kyd71JY4sv7rJSEGsIBgrY2NPFgdxz_EMFuDvlwxrEcb7g75ZAoKWqylCEynFOddMpL622DlgUWAxypbLQOvJTVRVcN3pflwnmHg5RCQfIGIZ_rxeNCzrjXzefa2GRFIZnywZ4WHl89Ob8BOBkpwet09WYYo6tk5B5VyD8fzu3qzDpHrIe9ndRgFtAv-_GjAvaCZCRQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+Performance+of+Sparse+Fast+Fourier+Transform+Algorithms+Using+the+Aliasing+Filter&rft.jtitle=Electronics+%28Basel%29&rft.au=Li%2C+Bin&rft.au=Jiang%2C+Zhikang&rft.au=Chen%2C+Jie&rft.date=2021-05-01&rft.issn=2079-9292&rft.eissn=2079-9292&rft.volume=10&rft.issue=9&rft.spage=1117&rft_id=info:doi/10.3390%2Felectronics10091117&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_electronics10091117
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2079-9292&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2079-9292&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2079-9292&client=summon