RSNS-to-Binary Conversion
The robust symmetrical number system (RSNS) is a symmetrical number system formed such that only one element in each RSNS vector changes between code transitions. This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and...
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| Veröffentlicht in: | IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 2007-09, Vol.54 (9), p.2030-2043 |
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| container_title | IEEE transactions on circuits and systems. 1, Fundamental theory and applications |
| container_volume | 54 |
| creator | Luke, B.L. Pace, P.E. |
| description | The robust symmetrical number system (RSNS) is a symmetrical number system formed such that only one element in each RSNS vector changes between code transitions. This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and electro-optical ADCs since it eliminates any encoding errors that can occur when the input signal lies about any code transition point. One of the fundamental difficulties in a hardware application of the RSNS, such as an ADC, is the conversion of the RSNS residue vectors into a more convenient representation such as a binary number. By exploiting the one-to-one correspondence between the RSNS and the residue number system, an efficient process for conversion of the symmetrical residues is formed. The conversion process presented in this paper produces a hardware implementation that is at least an order of magnitude smaller in terms of transistor count than read-only-memory conversion methods, and is easily pipelined to achieve fast conversion speeds. |
| doi_str_mv | 10.1109/TCSI.2007.904683 |
| format | Article |
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This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and electro-optical ADCs since it eliminates any encoding errors that can occur when the input signal lies about any code transition point. One of the fundamental difficulties in a hardware application of the RSNS, such as an ADC, is the conversion of the RSNS residue vectors into a more convenient representation such as a binary number. By exploiting the one-to-one correspondence between the RSNS and the residue number system, an efficient process for conversion of the symmetrical residues is formed. The conversion process presented in this paper produces a hardware implementation that is at least an order of magnitude smaller in terms of transistor count than read-only-memory conversion methods, and is easily pipelined to achieve fast conversion speeds.</description><identifier>ISSN: 1549-8328</identifier><identifier>ISSN: 1057-7122</identifier><identifier>EISSN: 1558-0806</identifier><identifier>DOI: 10.1109/TCSI.2007.904683</identifier><identifier>CODEN: ITCSCH</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Analog-digital conversion ; Antennas ; Architecture ; Circuit theory ; Conversion ; converters ; Data conversion ; Design engineering ; Digital signal processing ; Directive antennas ; Discrete Fourier transforms ; Dynamic range ; Encoding ; Hardware ; Mathematical analysis ; Number systems ; Residues ; robust symmetrical number systems (RSNSs) ; Robustness ; symmetry ; Vectors (mathematics)</subject><ispartof>IEEE transactions on circuits and systems. 1, Fundamental theory and applications, 2007-09, Vol.54 (9), p.2030-2043</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-44469770d1c6c537f8f9b0aaeaf498dc33d9cae5f2d15dbda648fc47363de6453</citedby><cites>FETCH-LOGICAL-c354t-44469770d1c6c537f8f9b0aaeaf498dc33d9cae5f2d15dbda648fc47363de6453</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4303303$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4303303$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Luke, B.L.</creatorcontrib><creatorcontrib>Pace, P.E.</creatorcontrib><title>RSNS-to-Binary Conversion</title><title>IEEE transactions on circuits and systems. 1, Fundamental theory and applications</title><addtitle>TCSI</addtitle><description>The robust symmetrical number system (RSNS) is a symmetrical number system formed such that only one element in each RSNS vector changes between code transitions. This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and electro-optical ADCs since it eliminates any encoding errors that can occur when the input signal lies about any code transition point. One of the fundamental difficulties in a hardware application of the RSNS, such as an ADC, is the conversion of the RSNS residue vectors into a more convenient representation such as a binary number. By exploiting the one-to-one correspondence between the RSNS and the residue number system, an efficient process for conversion of the symmetrical residues is formed. The conversion process presented in this paper produces a hardware implementation that is at least an order of magnitude smaller in terms of transistor count than read-only-memory conversion methods, and is easily pipelined to achieve fast conversion speeds.</description><subject>Analog-digital conversion</subject><subject>Antennas</subject><subject>Architecture</subject><subject>Circuit theory</subject><subject>Conversion</subject><subject>converters</subject><subject>Data conversion</subject><subject>Design engineering</subject><subject>Digital signal processing</subject><subject>Directive antennas</subject><subject>Discrete Fourier transforms</subject><subject>Dynamic range</subject><subject>Encoding</subject><subject>Hardware</subject><subject>Mathematical analysis</subject><subject>Number systems</subject><subject>Residues</subject><subject>robust symmetrical number systems (RSNSs)</subject><subject>Robustness</subject><subject>symmetry</subject><subject>Vectors (mathematics)</subject><issn>1549-8328</issn><issn>1057-7122</issn><issn>1558-0806</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kE1LAzEQhoMoWKt3xYt4EC-pk518HnXxo1AUbD2HNJuFLe2uJq3gvzfLigcPwsDM4XmHmYeQUwYTxsDcLMr5dFIAqIkBLjXukRETQlPQIPf7mRuqsdCH5CilFUBhANmInL3On-d029G7pnXx66Ls2s8QU9O1x-SgdusUTn76mLw93C_KJzp7eZyWtzPqUfAt5ZxLoxRUzEsvUNW6NktwLriaG115xMp4F0RdVExUy8pJrmvPFUqsguQCx-Rq2Pseu49dSFu7aZIP67VrQ7dLFjODgDqD1_-CTCrGURjVo5d_0FW3i21-w2rJjVQGMUMwQD52KcVQ2_fYbLIEy8D2Tm3v1PZO7eA0R86HSBNC-MV5Pq-vb6jmb7I</recordid><startdate>20070901</startdate><enddate>20070901</enddate><creator>Luke, B.L.</creator><creator>Pace, P.E.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20070901</creationdate><title>RSNS-to-Binary Conversion</title><author>Luke, B.L. ; Pace, P.E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-44469770d1c6c537f8f9b0aaeaf498dc33d9cae5f2d15dbda648fc47363de6453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Analog-digital conversion</topic><topic>Antennas</topic><topic>Architecture</topic><topic>Circuit theory</topic><topic>Conversion</topic><topic>converters</topic><topic>Data conversion</topic><topic>Design engineering</topic><topic>Digital signal processing</topic><topic>Directive antennas</topic><topic>Discrete Fourier transforms</topic><topic>Dynamic range</topic><topic>Encoding</topic><topic>Hardware</topic><topic>Mathematical analysis</topic><topic>Number systems</topic><topic>Residues</topic><topic>robust symmetrical number systems (RSNSs)</topic><topic>Robustness</topic><topic>symmetry</topic><topic>Vectors (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Luke, B.L.</creatorcontrib><creatorcontrib>Pace, P.E.</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>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on circuits and systems. 1, Fundamental theory and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Luke, B.L.</au><au>Pace, P.E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>RSNS-to-Binary Conversion</atitle><jtitle>IEEE transactions on circuits and systems. 1, Fundamental theory and applications</jtitle><stitle>TCSI</stitle><date>2007-09-01</date><risdate>2007</risdate><volume>54</volume><issue>9</issue><spage>2030</spage><epage>2043</epage><pages>2030-2043</pages><issn>1549-8328</issn><issn>1057-7122</issn><eissn>1558-0806</eissn><coden>ITCSCH</coden><abstract>The robust symmetrical number system (RSNS) is a symmetrical number system formed such that only one element in each RSNS vector changes between code transitions. This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and electro-optical ADCs since it eliminates any encoding errors that can occur when the input signal lies about any code transition point. One of the fundamental difficulties in a hardware application of the RSNS, such as an ADC, is the conversion of the RSNS residue vectors into a more convenient representation such as a binary number. By exploiting the one-to-one correspondence between the RSNS and the residue number system, an efficient process for conversion of the symmetrical residues is formed. 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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Analog-digital conversion Antennas Architecture Circuit theory Conversion converters Data conversion Design engineering Digital signal processing Directive antennas Discrete Fourier transforms Dynamic range Encoding Hardware Mathematical analysis Number systems Residues robust symmetrical number systems (RSNSs) Robustness symmetry Vectors (mathematics) |
| title | RSNS-to-Binary Conversion |
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