Armlets and balanced multiwavelets: flipping filter construction
In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the nonc...
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| Veröffentlicht in: | IEEE transactions on signal processing 2005-05, Vol.53 (5), p.1754-1767 |
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| creator | LIAN, Jian-Ao |
| description | In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets. |
| doi_str_mv | 10.1109/TSP.2005.845468 |
| format | Article |
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However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2005.845468</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Armlet ; balanced ; Balancing ; Construction ; Detection, estimation, filtering, equalization, prediction ; Digital filters ; Exact sciences and technology ; Finite impulse response filter ; Information, signal and communications theory ; Linear phase ; Mathematical analysis ; Mathematics ; Multiplication ; Multiresolution analysis ; multiwavelet ; Nonlinear filters ; orthogonality ; Polynomials ; scaling function vector ; Signal and communications theory ; Signal processing ; Signal, noise ; Symmetric matrices ; Telecommunications and information theory ; Vectors ; Vectors (mathematics) ; Wavelet ; Wavelet analysis</subject><ispartof>IEEE transactions on signal processing, 2005-05, Vol.53 (5), p.1754-1767</ispartof><rights>2005 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2005</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-821077a2b8139dc0ac7716113fd6b51cb53a3219a5e00adb61c09da622d427433</citedby><cites>FETCH-LOGICAL-c381t-821077a2b8139dc0ac7716113fd6b51cb53a3219a5e00adb61c09da622d427433</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1420815$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1420815$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16694308$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>LIAN, Jian-Ao</creatorcontrib><title>Armlets and balanced multiwavelets: flipping filter construction</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets.</description><subject>Applied sciences</subject><subject>Armlet</subject><subject>balanced</subject><subject>Balancing</subject><subject>Construction</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Digital filters</subject><subject>Exact sciences and technology</subject><subject>Finite impulse response filter</subject><subject>Information, signal and communications theory</subject><subject>Linear phase</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Multiplication</subject><subject>Multiresolution analysis</subject><subject>multiwavelet</subject><subject>Nonlinear filters</subject><subject>orthogonality</subject><subject>Polynomials</subject><subject>scaling function vector</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal, noise</subject><subject>Symmetric matrices</subject><subject>Telecommunications and information theory</subject><subject>Vectors</subject><subject>Vectors (mathematics)</subject><subject>Wavelet</subject><subject>Wavelet analysis</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kE1r3DAQhkVpoOkm5x5yMYUmJ29mJFkfPWVZ0iYQSCAb6E3IshwUvPZWshP67yuzgYUeepqBeeZl5iHkC8ISEfTl5vFhSQGqpeIVF-oDOUbNsQQuxcfcQ8XKSslfn8jnlF4AkHMtjsnVKm47P6bC9k1R2872zjfFdurG8GZf_Tz6XrRd2O1C_1y0oRt9LNzQpzFObgxDf0KOWtslf_peF-Tpx_VmfVPe3f-8Xa_uSscUjqWiCFJaWitkunFgnZQoEFnbiLpCV1fMMoraVh7ANrVAB7qxgtKGU8kZW5CLfe4uDr8nn0azDcn5Ll_shykZpQVKLnP8gpz_l6QKBAUlMvj1H_BlmGKfvzBKaGSo6Axd7iEXh5Sib80uhq2NfwyCmcWbLN7M4s1efN749h5rk7NdG7PTkA5rQmjOYObO9lzw3h_GPN-GFfsLbZ-KUQ</recordid><startdate>20050501</startdate><enddate>20050501</enddate><creator>LIAN, Jian-Ao</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></search><sort><creationdate>20050501</creationdate><title>Armlets and balanced multiwavelets: flipping filter construction</title><author>LIAN, Jian-Ao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-821077a2b8139dc0ac7716113fd6b51cb53a3219a5e00adb61c09da622d427433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Applied sciences</topic><topic>Armlet</topic><topic>balanced</topic><topic>Balancing</topic><topic>Construction</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>Digital filters</topic><topic>Exact sciences and technology</topic><topic>Finite impulse response filter</topic><topic>Information, signal and communications theory</topic><topic>Linear phase</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Multiplication</topic><topic>Multiresolution analysis</topic><topic>multiwavelet</topic><topic>Nonlinear filters</topic><topic>orthogonality</topic><topic>Polynomials</topic><topic>scaling function vector</topic><topic>Signal and communications theory</topic><topic>Signal processing</topic><topic>Signal, noise</topic><topic>Symmetric matrices</topic><topic>Telecommunications and information theory</topic><topic>Vectors</topic><topic>Vectors (mathematics)</topic><topic>Wavelet</topic><topic>Wavelet analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>LIAN, Jian-Ao</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><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>LIAN, Jian-Ao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Armlets and balanced multiwavelets: flipping filter construction</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2005-05-01</date><risdate>2005</risdate><volume>53</volume><issue>5</issue><spage>1754</spage><epage>1767</epage><pages>1754-1767</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2005.845468</doi><tpages>14</tpages></addata></record> |
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| subjects | Applied sciences Armlet balanced Balancing Construction Detection, estimation, filtering, equalization, prediction Digital filters Exact sciences and technology Finite impulse response filter Information, signal and communications theory Linear phase Mathematical analysis Mathematics Multiplication Multiresolution analysis multiwavelet Nonlinear filters orthogonality Polynomials scaling function vector Signal and communications theory Signal processing Signal, noise Symmetric matrices Telecommunications and information theory Vectors Vectors (mathematics) Wavelet Wavelet analysis |
| title | Armlets and balanced multiwavelets: flipping filter construction |
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