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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">sibsutis</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник СибГУТИ</journal-title><trans-title-group xml:lang="en"><trans-title>The Herald of the Siberian State University of Telecommunications and Information Science</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1998-6920</issn><publisher><publisher-name>СибГУТИ</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">sibsutis-479</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Оценка точности алгоритмов восстановления дискретных сигналов, заданных на неравномерной временной сетке с точно неизвестными значениями координат узлов</article-title><trans-title-group xml:lang="en"><trans-title>Research of optimization methods for the reconstruction of irregularly sampled discrete-time signals with unknown sampling locations</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Поршнев</surname><given-names>С. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Porshnev</surname><given-names>S. ..</given-names></name></name-alternatives><email xlink:type="simple">sergey_porshnev@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кусайкин</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kusaykin</surname><given-names>D. ..</given-names></name></name-alternatives><email xlink:type="simple">kusaykin@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff xml:lang="ru" id="aff-1"><institution>УрФУ; ФГОБУ ВПО «СибГУТИ»</institution><country>Russian Federation</country></aff><aff xml:lang="ru" id="aff-2"><institution>ФГОБУ ВПО «СибГУТИ»</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>26</day><month>10</month><year>2022</year></pub-date><volume>0</volume><issue>1</issue><fpage>97</fpage><lpage>108</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Поршнев С.В., Кусайкин Д.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Поршнев С.В., Кусайкин Д.В.</copyright-holder><copyright-holder xml:lang="en">Porshnev S..., Kusaykin D...</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.sibsutis.ru/jour/article/view/479">https://vestnik.sibsutis.ru/jour/article/view/479</self-uri><abstract><p>В статье обсуждаются результаты исследования возможности восстановления дискретных сигналов (ДС), заданных на неравномерной временно́й сетке t7- = iT + τέ,   i = 1,2,3..., где T - период дискретизации; τ - случайное число, точное значение которого неизвестно (джиттер),  τ є(-T/2, T/2). Изучены известные оптимизационные методы, разработанные для оценивания значений джиттера. Получены оценки точности восстановления дискретных сигналов при определении значений координат узлов временной сетки рассматриваемыми методами.</p></abstract><trans-abstract xml:lang="en"><p>In this paper we consider investigation findings of reconstruction methods of non-uniform discrete-time signals with unknown sampling locations. In sampling applications the set on which a signal is sampled is t7- = iT + τέ,   i = 1,2,3,..., T - sampling period; τ - jitter- a random number τ є(-T/2, T/2), the exact value of which is not known. The present optimization methods of finding unknown non-uniform sample locations are identified. Reconstruction errors of the methods of finding unknown non-uniform sample locations are presented.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>неравномерная дискретизация</kwd><kwd>восстановление дискретных сигналов</kwd><kwd>неизвестные местоположения отсчётов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>non-uniform sampling</kwd><kwd>irregular sampling</kwd><kwd>reconstruction</kwd><kwd>unknown sampling locations</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Divi V., Wornell G. Signal recovery in time-interleaved analog-to-digital converters // Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 2004, P. 593-596.</mixed-citation><mixed-citation xml:lang="en">Divi V., Wornell G. Signal recovery in time-interleaved analog-to-digital converters // Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 2004, P. 593-596.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Ahmad, Bashar I. Applications of nonuniform sampling in wideband multi-channel communication systems. PhD thesis, University of Westminster, School of Electronics and Computer Science, 2011. P.180.</mixed-citation><mixed-citation xml:lang="en">Ahmad, Bashar I. Applications of nonuniform sampling in wideband multi-channel communication systems. PhD thesis, University of Westminster, School of Electronics and Computer Science, 2011. P.180.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Unser M. Sampling -50 years after Shannon //Proceedings of the IEEE, 2000, vol. 88, no. 4.P. 569-587.</mixed-citation><mixed-citation xml:lang="en">Unser M. Sampling -50 years after Shannon //Proceedings of the IEEE, 2000, vol. 88, no. 4.P. 569-587.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Yen. J. L. On Nonuniform sampling of bandwidth-limited signals. / IRE Transactions on Circuit Theory CT-3.1956, pp. 251-259.</mixed-citation><mixed-citation xml:lang="en">Yen. J. L. On Nonuniform sampling of bandwidth-limited signals. / IRE Transactions on Circuit Theory CT-3.1956, pp. 251-259.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Shapiro H. S. Alias free sampling of random noise / H. S. Shapiro, R. A. Silverman // Journal Society for Industrial and Applied Mathematics. 1960.Vol. 8, no. 2, pp. 225-248.</mixed-citation><mixed-citation xml:lang="en">Shapiro H. S. Alias free sampling of random noise / H. S. Shapiro, R. A. Silverman // Journal Society for Industrial and Applied Mathematics. 1960.Vol. 8, no. 2, pp. 225-248.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Горелов Г.В. Нерегулярная дискретизация сигналов / Г.В. Горелов. - М.: Радиоисвязь, 1982. - 256 с.</mixed-citation><mixed-citation xml:lang="en">Горелов Г.В. Нерегулярная дискретизация сигналов / Г.В. Горелов. - М.: Радиоисвязь, 1982. - 256 с.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Билинский, И. Я. Стохастическая цифровая обработка непрерывных сигналов / И. Я. Билинский, А. К. Микелсон. - Рига: Зинатне, 1983. - 292 с.</mixed-citation><mixed-citation xml:lang="en">Билинский, И. Я. Стохастическая цифровая обработка непрерывных сигналов / И. Я. Билинский, А. К. Микелсон. - Рига: Зинатне, 1983. - 292 с.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Feichtinger H.G., Grochenig K., Strohmer T. Efficient numerical methods in non-uniform sampling theory // Numerische Mathematik, 1995. No 69. P. 423-440.</mixed-citation><mixed-citation xml:lang="en">Feichtinger H.G., Grochenig K., Strohmer T. Efficient numerical methods in non-uniform sampling theory // Numerische Mathematik, 1995. No 69. P. 423-440.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Senay S. Signal reconstruction from nonuniform samples using prolate spheroidal wave functions: theory and application. Doctoral Dissertation, Pittsburgh. 2011. P. 117.</mixed-citation><mixed-citation xml:lang="en">Senay S. Signal reconstruction from nonuniform samples using prolate spheroidal wave functions: theory and application. Doctoral Dissertation, Pittsburgh. 2011. P. 117.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Selva. J. Functionally weighted Lagrange interpolation of band-limited signals from nonuniform samples // IEEE Transactions on Signal Processing. 2009. V. 57, №1. P.168-181.</mixed-citation><mixed-citation xml:lang="en">Selva. J. Functionally weighted Lagrange interpolation of band-limited signals from nonuniform samples // IEEE Transactions on Signal Processing. 2009. V. 57, №1. P.168-181.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Browning J. A method of finding unknown continuous-time nonuniform sample locations of band-limited functions // Advanced Signal Processing Algorithms, Architectures, and Implementations XIV. Edited by Luk, Franklin T. Proceedings of the SPIE. 2004. Vol. 5559. P. 289-296.</mixed-citation><mixed-citation xml:lang="en">Browning J. A method of finding unknown continuous-time nonuniform sample locations of band-limited functions // Advanced Signal Processing Algorithms, Architectures, and Implementations XIV. Edited by Luk, Franklin T. Proceedings of the SPIE. 2004. Vol. 5559. P. 289-296.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Browning J. Approximating Signals From Nonuniform Continuous Time Samples at Unknown Locations // IEEE Transactions on Signal Processing. 2007. Vol. 55, no. 4. P. 1549 - 1554.</mixed-citation><mixed-citation xml:lang="en">Browning J. Approximating Signals From Nonuniform Continuous Time Samples at Unknown Locations // IEEE Transactions on Signal Processing. 2007. Vol. 55, no. 4. P. 1549 - 1554.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Marziliano P., Vetterli M. Irregular sampling with unknown locations // IEEE International Conference on Acoustics, Speech, and Signal Processing, 1999, vol. 3. P. 1657 - 1660.</mixed-citation><mixed-citation xml:lang="en">Marziliano P., Vetterli M. Irregular sampling with unknown locations // IEEE International Conference on Acoustics, Speech, and Signal Processing, 1999, vol. 3. P. 1657 - 1660.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Marziliano P., Vetterli M. Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations // IEEE Transactions on Signal Processing, 2000, vol. 48, Issue 12.P. 3462 - 3471.</mixed-citation><mixed-citation xml:lang="en">Marziliano P., Vetterli M. Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations // IEEE Transactions on Signal Processing, 2000, vol. 48, Issue 12.P. 3462 - 3471.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Marziliano P. Sampling Innovations./PhD. Thesis, Swiss Federal Institute of Technology Lausanne, Switzerland, 2001. no. 2369.</mixed-citation><mixed-citation xml:lang="en">Marziliano P. Sampling Innovations./PhD. Thesis, Swiss Federal Institute of Technology Lausanne, Switzerland, 2001. no. 2369.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Половко А.М. Интерполяция. Методы и компьютерные технологии их реализации / А.М. Половко, П.Н. Бутусов; - СПб.: БХВ-Петербург, 2004. - 320 с.</mixed-citation><mixed-citation xml:lang="en">Половко А.М. Интерполяция. Методы и компьютерные технологии их реализации / А.М. Половко, П.Н. Бутусов; - СПб.: БХВ-Петербург, 2004. - 320 с.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Поршнев С.В., Кусайкин Д.В. Исследование точности методов восстановления дискретных сигналов, заданных на неравномерной временно́й сетке // В мире научных открытий. - 2013. - Т. 46, № 10.С. 261-279.</mixed-citation><mixed-citation xml:lang="en">Поршнев С.В., Кусайкин Д.В. Исследование точности методов восстановления дискретных сигналов, заданных на неравномерной временно́й сетке // В мире научных открытий. - 2013. - Т. 46, № 10.С. 261-279.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
