Exact interpolation and iterative subdivision schemes
We examine the circumstances under which a discrete-time signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and suffici...
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| Veröffentlicht in: | IEEE transactions on signal processing 1995-06, Vol.43 (6), p.1348-1359 |
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| container_title | IEEE transactions on signal processing |
| container_volume | 43 |
| creator | Herley, C. |
| description | We examine the circumstances under which a discrete-time signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. A better criterion is to use interpolators that are exact for polynomial functions. We demonstrate that these interpolators converge when iterated, and show how these may be designed for any polynomial degree N and any interpolation factor M. This makes it possible to design interpolators for iterative schemes to make best use of the resolution available in a given display medium.< > |
| doi_str_mv | 10.1109/78.388849 |
| format | Article |
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After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. A better criterion is to use interpolators that are exact for polynomial functions. We demonstrate that these interpolators converge when iterated, and show how these may be designed for any polynomial degree N and any interpolation factor M. This makes it possible to design interpolators for iterative schemes to make best use of the resolution available in a given display medium.< ></description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/78.388849</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Displays ; Exact sciences and technology ; Filter bank ; Information, signal and communications theory ; Interpolation ; Mathematical methods ; Maximum likelihood detection ; Polynomials ; Shape ; Signal design ; Signal resolution ; Sufficient conditions ; Telecommunications and information theory</subject><ispartof>IEEE transactions on signal processing, 1995-06, Vol.43 (6), p.1348-1359</ispartof><rights>1995 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c306t-87dc998276a87ad72aa5aa899c6786c911ab7f12b649a356d0f8f4999988605b3</citedby><cites>FETCH-LOGICAL-c306t-87dc998276a87ad72aa5aa899c6786c911ab7f12b649a356d0f8f4999988605b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/388849$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/388849$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3571321$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Herley, C.</creatorcontrib><title>Exact interpolation and iterative subdivision schemes</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>We examine the circumstances under which a discrete-time signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. A better criterion is to use interpolators that are exact for polynomial functions. We demonstrate that these interpolators converge when iterated, and show how these may be designed for any polynomial degree N and any interpolation factor M. This makes it possible to design interpolators for iterative schemes to make best use of the resolution available in a given display medium.< ></description><subject>Applied sciences</subject><subject>Displays</subject><subject>Exact sciences and technology</subject><subject>Filter bank</subject><subject>Information, signal and communications theory</subject><subject>Interpolation</subject><subject>Mathematical methods</subject><subject>Maximum likelihood detection</subject><subject>Polynomials</subject><subject>Shape</subject><subject>Signal design</subject><subject>Signal resolution</subject><subject>Sufficient conditions</subject><subject>Telecommunications and information theory</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNpFkEtLAzEUhYMoWKsLt65mIYKLqcnkdbOUUh9QcKPgLtzJZDAyjzqZFv33pkzRu7mP892zOIRcMrpgjJo7DQsOAMIckRkzguVUaHWcZip5LkG_n5KzGD8pZUIYNSNy9Y1uzEI3-mHTNziGvsuwq7KQDmnb-SxuyyrsQtwr0X341sdzclJjE_3Foc_J28PqdfmUr18en5f369xxqsYcdOWMgUIrBI2VLhAlIhjjlAblDGNY6poVpRIGuVQVraEWJhWAorLkc3Iz-W6G_mvr42jbEJ1vGux8v422AKUZLWgCbyfQDX2Mg6_tZggtDj-WUbsPxmqwUzCJvT6YYnTY1AN2LsS_By414wVL2NWEBe_9vzp5_ALmz2m4</recordid><startdate>19950601</startdate><enddate>19950601</enddate><creator>Herley, C.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19950601</creationdate><title>Exact interpolation and iterative subdivision schemes</title><author>Herley, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c306t-87dc998276a87ad72aa5aa899c6786c911ab7f12b649a356d0f8f4999988605b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>Applied sciences</topic><topic>Displays</topic><topic>Exact sciences and technology</topic><topic>Filter bank</topic><topic>Information, signal and communications theory</topic><topic>Interpolation</topic><topic>Mathematical methods</topic><topic>Maximum likelihood detection</topic><topic>Polynomials</topic><topic>Shape</topic><topic>Signal design</topic><topic>Signal resolution</topic><topic>Sufficient conditions</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Herley, C.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems 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><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Herley, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact interpolation and iterative subdivision schemes</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>1995-06-01</date><risdate>1995</risdate><volume>43</volume><issue>6</issue><spage>1348</spage><epage>1359</epage><pages>1348-1359</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>We examine the circumstances under which a discrete-time signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. A better criterion is to use interpolators that are exact for polynomial functions. We demonstrate that these interpolators converge when iterated, and show how these may be designed for any polynomial degree N and any interpolation factor M. This makes it possible to design interpolators for iterative schemes to make best use of the resolution available in a given display medium.< ></abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/78.388849</doi><tpages>12</tpages></addata></record> |
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| identifier | ISSN: 1053-587X |
| ispartof | IEEE transactions on signal processing, 1995-06, Vol.43 (6), p.1348-1359 |
| issn | 1053-587X 1941-0476 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_3571321 |
| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Displays Exact sciences and technology Filter bank Information, signal and communications theory Interpolation Mathematical methods Maximum likelihood detection Polynomials Shape Signal design Signal resolution Sufficient conditions Telecommunications and information theory |
| title | Exact interpolation and iterative subdivision schemes |
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