One or Two Frequencies? The Empirical Mode Decomposition Answers
This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whet...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on signal processing 2008-01, Vol.56 (1), p.85-95 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 95 |
|---|---|
| container_issue | 1 |
| container_start_page | 85 |
| container_title | IEEE transactions on signal processing |
| container_volume | 56 |
| creator | Rilling, G. Flandrin, P. |
| description | This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed. |
| doi_str_mv | 10.1109/TSP.2007.906771 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_proquest_journals_863203044</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>4359551</ieee_id><sourcerecordid>889378136</sourcerecordid><originalsourceid>FETCH-LOGICAL-c503t-72cc16e9b957a356cb73c1817f0fb793eb1a464913dc74d45a15702c5c73ecd03</originalsourceid><addsrcrecordid>eNp90U1LJDEQBuBGVtBVzx720izsCgs9VnW-OqfdwW8YUXAEbyGTqcZIT2dMZlb892ZocWEPnhLIU0Wq3qI4RBghgj6e3t2OagA10iCVwq1iFzXHCriSX_IdBKtEox52iq8pPQEg51ruFn9ueipDLKcvoTyP9Lym3nlKv8vpI5Vni6WP3tmuvA5zKk_JhcUyJL_yoS_HfXqhmPaL7dZ2iQ7ez73i_vxsenJZTW4urk7Gk8oJYKtK1c6hJD3TQlkmpJsp5rBB1UI7U5rRDC2XXCObO8XnXFgUCmonnGLk5sD2il9D30fbmWX0CxtfTbDeXI4nhvrUGUBd5zH1X8z4aMDLGPJIaWUWPjnqOttTWCfTNJqpBpnM8uenkvFGy6bmGX7_Dz6FdezzyKaRrAYGfIOOB-RiSClS-_FTBLNJyeSUzCYlM6SUK368t7UpL7qNNu8__SvTWjCBOrtvg_NE9PHMmdBCIHsDeUuXmA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>863203044</pqid></control><display><type>article</type><title>One or Two Frequencies? The Empirical Mode Decomposition Answers</title><source>IEEE Electronic Library (IEL)</source><creator>Rilling, G. ; Flandrin, P.</creator><creatorcontrib>Rilling, G. ; Flandrin, P.</creatorcontrib><description>This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2007.906771</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Amplitude estimation ; Amplitude modulation ; Amplitudes ; Applied sciences ; Computer Science ; Decomposition ; Ear ; Empirical analysis ; Empirical mode decomposition (EMD) ; Engineering Sciences ; Exact sciences and technology ; Frequency estimation ; Humans ; Information, signal and communications theory ; Mathematical models ; Nonlinearity ; Physics ; resolution ; Signal analysis ; Signal and communications theory ; Signal and Image Processing ; Signal processing ; Signal representation. Spectral analysis ; Signal resolution ; Signal, noise ; Spectral analysis ; Telecommunications and information theory ; time frequency ; Time frequency analysis ; Unity ; Waveforms</subject><ispartof>IEEE transactions on signal processing, 2008-01, Vol.56 (1), p.85-95</ispartof><rights>2008 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c503t-72cc16e9b957a356cb73c1817f0fb793eb1a464913dc74d45a15702c5c73ecd03</citedby><cites>FETCH-LOGICAL-c503t-72cc16e9b957a356cb73c1817f0fb793eb1a464913dc74d45a15702c5c73ecd03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4359551$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,885,4024,27923,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4359551$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19953519$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://ens-lyon.hal.science/ensl-01921059$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Rilling, G.</creatorcontrib><creatorcontrib>Flandrin, P.</creatorcontrib><title>One or Two Frequencies? The Empirical Mode Decomposition Answers</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed.</description><subject>Amplitude estimation</subject><subject>Amplitude modulation</subject><subject>Amplitudes</subject><subject>Applied sciences</subject><subject>Computer Science</subject><subject>Decomposition</subject><subject>Ear</subject><subject>Empirical analysis</subject><subject>Empirical mode decomposition (EMD)</subject><subject>Engineering Sciences</subject><subject>Exact sciences and technology</subject><subject>Frequency estimation</subject><subject>Humans</subject><subject>Information, signal and communications theory</subject><subject>Mathematical models</subject><subject>Nonlinearity</subject><subject>Physics</subject><subject>resolution</subject><subject>Signal analysis</subject><subject>Signal and communications theory</subject><subject>Signal and Image Processing</subject><subject>Signal processing</subject><subject>Signal representation. Spectral analysis</subject><subject>Signal resolution</subject><subject>Signal, noise</subject><subject>Spectral analysis</subject><subject>Telecommunications and information theory</subject><subject>time frequency</subject><subject>Time frequency analysis</subject><subject>Unity</subject><subject>Waveforms</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90U1LJDEQBuBGVtBVzx720izsCgs9VnW-OqfdwW8YUXAEbyGTqcZIT2dMZlb892ZocWEPnhLIU0Wq3qI4RBghgj6e3t2OagA10iCVwq1iFzXHCriSX_IdBKtEox52iq8pPQEg51ruFn9ueipDLKcvoTyP9Lym3nlKv8vpI5Vni6WP3tmuvA5zKk_JhcUyJL_yoS_HfXqhmPaL7dZ2iQ7ez73i_vxsenJZTW4urk7Gk8oJYKtK1c6hJD3TQlkmpJsp5rBB1UI7U5rRDC2XXCObO8XnXFgUCmonnGLk5sD2il9D30fbmWX0CxtfTbDeXI4nhvrUGUBd5zH1X8z4aMDLGPJIaWUWPjnqOttTWCfTNJqpBpnM8uenkvFGy6bmGX7_Dz6FdezzyKaRrAYGfIOOB-RiSClS-_FTBLNJyeSUzCYlM6SUK368t7UpL7qNNu8__SvTWjCBOrtvg_NE9PHMmdBCIHsDeUuXmA</recordid><startdate>200801</startdate><enddate>200801</enddate><creator>Rilling, G.</creator><creator>Flandrin, P.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope><scope>1XC</scope></search><sort><creationdate>200801</creationdate><title>One or Two Frequencies? The Empirical Mode Decomposition Answers</title><author>Rilling, G. ; Flandrin, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c503t-72cc16e9b957a356cb73c1817f0fb793eb1a464913dc74d45a15702c5c73ecd03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Amplitude estimation</topic><topic>Amplitude modulation</topic><topic>Amplitudes</topic><topic>Applied sciences</topic><topic>Computer Science</topic><topic>Decomposition</topic><topic>Ear</topic><topic>Empirical analysis</topic><topic>Empirical mode decomposition (EMD)</topic><topic>Engineering Sciences</topic><topic>Exact sciences and technology</topic><topic>Frequency estimation</topic><topic>Humans</topic><topic>Information, signal and communications theory</topic><topic>Mathematical models</topic><topic>Nonlinearity</topic><topic>Physics</topic><topic>resolution</topic><topic>Signal analysis</topic><topic>Signal and communications theory</topic><topic>Signal and Image Processing</topic><topic>Signal processing</topic><topic>Signal representation. Spectral analysis</topic><topic>Signal resolution</topic><topic>Signal, noise</topic><topic>Spectral analysis</topic><topic>Telecommunications and information theory</topic><topic>time frequency</topic><topic>Time frequency analysis</topic><topic>Unity</topic><topic>Waveforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rilling, G.</creatorcontrib><creatorcontrib>Flandrin, P.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005–Present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Rilling, G.</au><au>Flandrin, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>One or Two Frequencies? The Empirical Mode Decomposition Answers</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2008-01</date><risdate>2008</risdate><volume>56</volume><issue>1</issue><spage>85</spage><epage>95</epage><pages>85-95</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2007.906771</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 1053-587X |
| ispartof | IEEE transactions on signal processing, 2008-01, Vol.56 (1), p.85-95 |
| issn | 1053-587X 1941-0476 |
| language | eng |
| recordid | cdi_proquest_journals_863203044 |
| source | IEEE Electronic Library (IEL) |
| subjects | Amplitude estimation Amplitude modulation Amplitudes Applied sciences Computer Science Decomposition Ear Empirical analysis Empirical mode decomposition (EMD) Engineering Sciences Exact sciences and technology Frequency estimation Humans Information, signal and communications theory Mathematical models Nonlinearity Physics resolution Signal analysis Signal and communications theory Signal and Image Processing Signal processing Signal representation. Spectral analysis Signal resolution Signal, noise Spectral analysis Telecommunications and information theory time frequency Time frequency analysis Unity Waveforms |
| title | One or Two Frequencies? The Empirical Mode Decomposition Answers |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T06%3A14%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=One%20or%20Two%20Frequencies?%20The%20Empirical%20Mode%20Decomposition%20Answers&rft.jtitle=IEEE%20transactions%20on%20signal%20processing&rft.au=Rilling,%20G.&rft.date=2008-01&rft.volume=56&rft.issue=1&rft.spage=85&rft.epage=95&rft.pages=85-95&rft.issn=1053-587X&rft.eissn=1941-0476&rft.coden=ITPRED&rft_id=info:doi/10.1109/TSP.2007.906771&rft_dat=%3Cproquest_RIE%3E889378136%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=863203044&rft_id=info:pmid/&rft_ieee_id=4359551&rfr_iscdi=true |