New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms
The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel...
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| Veröffentlicht in: | Signal processing 2010-03, Vol.90 (3), p.933-945 |
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| creator | Liu, Yue-Lin Kou, Kit-Ian Ho, Io-Tong |
| description | The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as special cases of the LCT. In this paper, we structure certain types of non-bandlimited signals based on two ladder-shape filters designed in the LCT domain. Subsequently, these non-bandlimited signals are reconstructed from their samples together with the generalized sinc function, their parameter
M-Hilbert transforms or their first derivatives and other information provided by the phase function of the nonlinear Fourier atom which is the boundary value of the
Möbius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established. |
| doi_str_mv | 10.1016/j.sigpro.2009.09.030 |
| format | Article |
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M-Hilbert transforms or their first derivatives and other information provided by the phase function of the nonlinear Fourier atom which is the boundary value of the
Möbius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established.</description><identifier>ISSN: 0165-1684</identifier><identifier>EISSN: 1872-7557</identifier><identifier>DOI: 10.1016/j.sigpro.2009.09.030</identifier><identifier>CODEN: SPRODR</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Applied sciences ; Derivatives ; Exact sciences and technology ; Fourier analysis ; Fourier transforms ; Generalized sinc function ; Information, signal and communications theory ; Linear canonical transform ; Mathematical analysis ; Non-bandlimited signal ; Nonlinearity ; Parameter M-Hilbert transform ; Pattern recognition ; Sampling ; Sampling theorem ; Sampling, quantization ; Signal and communications theory ; Signal processing ; Telecommunications and information theory ; Transforms</subject><ispartof>Signal processing, 2010-03, Vol.90 (3), p.933-945</ispartof><rights>2009 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c368t-421d3d6b77b9eab7c7d1baacf27177b594aff7d44866a51ebea5b535e2fbec593</citedby><cites>FETCH-LOGICAL-c368t-421d3d6b77b9eab7c7d1baacf27177b594aff7d44866a51ebea5b535e2fbec593</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0165168409004216$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22171047$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Yue-Lin</creatorcontrib><creatorcontrib>Kou, Kit-Ian</creatorcontrib><creatorcontrib>Ho, Io-Tong</creatorcontrib><title>New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms</title><title>Signal processing</title><description>The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as special cases of the LCT. In this paper, we structure certain types of non-bandlimited signals based on two ladder-shape filters designed in the LCT domain. Subsequently, these non-bandlimited signals are reconstructed from their samples together with the generalized sinc function, their parameter
M-Hilbert transforms or their first derivatives and other information provided by the phase function of the nonlinear Fourier atom which is the boundary value of the
Möbius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established.</description><subject>Applied sciences</subject><subject>Derivatives</subject><subject>Exact sciences and technology</subject><subject>Fourier analysis</subject><subject>Fourier transforms</subject><subject>Generalized sinc function</subject><subject>Information, signal and communications theory</subject><subject>Linear canonical transform</subject><subject>Mathematical analysis</subject><subject>Non-bandlimited signal</subject><subject>Nonlinearity</subject><subject>Parameter M-Hilbert transform</subject><subject>Pattern recognition</subject><subject>Sampling</subject><subject>Sampling theorem</subject><subject>Sampling, quantization</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Telecommunications and information theory</subject><subject>Transforms</subject><issn>0165-1684</issn><issn>1872-7557</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAQxYMouK5-Aw-5iKeuSds07UUQcVUQveg5TNPpmqVt1kzXP9_elF08CgMJw--9xzzGzqVYSCGLq_WC3GoT_CIVolpMk4kDNpOlThOtlD5ks4ipRBZlfsxOiNZCCJkVYsa-n_GLE_Sbzg0r3vrQbzvA6cMHPyQ1DE3nejdiw2PGAB1xIPLWwbT6cuM7j0qEwC1EgbPQ8THAQJMVj-rJZk8s_TY4DBxG39MpO2qjG57t3zl7W9693j4kTy_3j7c3T4nNinJM8lQ2WVPUWtcVQq2tbmQNYNtUy7hTVQ5tq5s8L4sClMQaQdUqU5i2NVpVZXN2ufON_XxskUbTO7LYdTCg35KphNQiLcsykvmOtMETBWzNJrgewo-Rwkw9m7XZ9Wymns00mYiyi30AULy-jcdbR3_aNJVailxH7nrHYbz2M_ZgyDocLDYuoB1N493_Qb_4Zplw</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>Liu, Yue-Lin</creator><creator>Kou, Kit-Ian</creator><creator>Ho, Io-Tong</creator><general>Elsevier B.V</general><general>Elsevier</general><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></search><sort><creationdate>20100301</creationdate><title>New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms</title><author>Liu, Yue-Lin ; Kou, Kit-Ian ; Ho, Io-Tong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-421d3d6b77b9eab7c7d1baacf27177b594aff7d44866a51ebea5b535e2fbec593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applied sciences</topic><topic>Derivatives</topic><topic>Exact sciences and technology</topic><topic>Fourier analysis</topic><topic>Fourier transforms</topic><topic>Generalized sinc function</topic><topic>Information, signal and communications theory</topic><topic>Linear canonical transform</topic><topic>Mathematical analysis</topic><topic>Non-bandlimited signal</topic><topic>Nonlinearity</topic><topic>Parameter M-Hilbert transform</topic><topic>Pattern recognition</topic><topic>Sampling</topic><topic>Sampling theorem</topic><topic>Sampling, quantization</topic><topic>Signal and communications theory</topic><topic>Signal processing</topic><topic>Telecommunications and information theory</topic><topic>Transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Yue-Lin</creatorcontrib><creatorcontrib>Kou, Kit-Ian</creatorcontrib><creatorcontrib>Ho, Io-Tong</creatorcontrib><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><jtitle>Signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Yue-Lin</au><au>Kou, Kit-Ian</au><au>Ho, Io-Tong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms</atitle><jtitle>Signal processing</jtitle><date>2010-03-01</date><risdate>2010</risdate><volume>90</volume><issue>3</issue><spage>933</spage><epage>945</epage><pages>933-945</pages><issn>0165-1684</issn><eissn>1872-7557</eissn><coden>SPRODR</coden><abstract>The sampling theory is basic and crucial in engineering sciences. 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M-Hilbert transforms or their first derivatives and other information provided by the phase function of the nonlinear Fourier atom which is the boundary value of the
Möbius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.sigpro.2009.09.030</doi><tpages>13</tpages></addata></record> |
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| ispartof | Signal processing, 2010-03, Vol.90 (3), p.933-945 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Applied sciences Derivatives Exact sciences and technology Fourier analysis Fourier transforms Generalized sinc function Information, signal and communications theory Linear canonical transform Mathematical analysis Non-bandlimited signal Nonlinearity Parameter M-Hilbert transform Pattern recognition Sampling Sampling theorem Sampling, quantization Signal and communications theory Signal processing Telecommunications and information theory Transforms |
| title | New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms |
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