{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T08:34:06Z","timestamp":1721810046772},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p> We consider the approximate consistent sampling process in the space L<jats:sup>2<\/jats:sup>(\u211d) of signals of finite energy, where multi-, pre- and post-filters [Formula: see text] and [Formula: see text] are from L<jats:sup>2<\/jats:sup>(\u211d). We take {(f * h<jats:sub>i<\/jats:sub>)(qk)| 1 \u2264 i \u2264 M, k \u2208 \u2124} as measurements(or generalized samples) of an input signal f and then seek its consistent approximation [Formula: see text] in the reconstruction space V(\u03a6), which is a shift-invariant subspace of L<jats:sup>2<\/jats:sup>(\u211d) generated by N post-filters [Formula: see text]. Here [Formula: see text] is a rational number and the consistency means that f and [Formula: see text] have the same measurements. We find equivalent conditions for the existence of such consistent approximation in L<jats:sup>2<\/jats:sup>(\u211d) together with some relevant properties such as performance analysis. <\/jats:p>","DOI":"10.1142\/s0219691313500082","type":"journal-article","created":{"date-parts":[[2013,1,3]],"date-time":"2013-01-03T09:10:34Z","timestamp":1357204234000},"page":"1350008","source":"Crossref","is-referenced-by-count":2,"title":["CONSISTENT SAMPLING WITH MULTI-, PRE- AND POST-FILTERINGS"],"prefix":"10.1142","volume":"11","author":[{"given":"AKIRA","family":"HIRABAYASHI","sequence":"first","affiliation":[{"name":"Department of Information Science and Engineering, Yamaguchi University, 2-16-1 Tokiwadai, Ube 755-8611, Japan"}]},{"given":"KIL HYUN","family":"KWON","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea"}]},{"given":"JAEKYU","family":"LEE","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea"}]}],"member":"219","published-online":{"date-parts":[[2013,3,11]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03255-8"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144501386986"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/01630569408816545"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8224-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2003.12.003"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/78.720386"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-003-0004-2"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8212-5_2"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1155\/ASP\/2006\/92674"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2006.873488"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691305000890"},{"key":"rf12","volume-title":"Matrix Computations","author":"Golub G.","year":"1996"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.895996"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S021969130800232X"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.11.005"},{"key":"rf16","first-page":"1163","volume":"93","author":"Kwon K. 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