{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T18:44:17Z","timestamp":1785955457162,"version":"3.56.0"},"reference-count":31,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[1962,12,1]],"date-time":"1962-12-01T00:00:00Z","timestamp":-223603200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2014,5,15]],"date-time":"2014-05-15T00:00:00Z","timestamp":1400112000000},"content-version":"vor","delay-in-days":18793,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information and Control"],"published-print":{"date-parts":[[1962,12]]},"DOI":"10.1016\/s0019-9958(62)90633-2","type":"journal-article","created":{"date-parts":[[2004,12,15]],"date-time":"2004-12-15T09:12:12Z","timestamp":1103101932000},"page":"279-323","source":"Crossref","is-referenced-by-count":509,"title":["Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces"],"prefix":"10.1016","volume":"5","author":[{"given":"Daniel P.","family":"Petersen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Middleton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0019-9958(62)90633-2_bib1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1109\/TIT.1957.1057404","article-title":"A note on the sampling principle for continuous signals","volume":"IT-3","author":"Balakrishnan","year":"1957","journal-title":"IRE Trans. on Information Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1071\/PH560297","article-title":"Two dimensional aerial smoothing in radio astronomy","volume":"9","author":"Bracewell","year":"1956","journal-title":"Australian J. Phys."},{"key":"10.1016\/S0019-9958(62)90633-2_bib3","first-page":"105","article-title":"Science and Information Theory","author":"Brillouin","year":"1956"},{"key":"10.1016\/S0019-9958(62)90633-2_bib4","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TIT.1961.1057649","article-title":"Optimum prefiltering of sampled data","volume":"IT-7","author":"Brown","year":"1961","journal-title":"IRE Trans. on Information Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib5","first-page":"538","article-title":"Optimum transmission of continuous signal over a sampled data link","volume":"79","author":"Chang","year":"1961","journal-title":"AIEE Trans. II"},{"key":"10.1016\/S0019-9958(62)90633-2_bib6","doi-asserted-by":"crossref","first-page":"391","DOI":"10.4153\/CJM-1951-045-8","article-title":"Extreme forms","volume":"3","author":"Coxeter","year":"1951","journal-title":"Can. J. Math."},{"key":"10.1016\/S0019-9958(62)90633-2_bib7","first-page":"96","article-title":"An Introduction to the Theory of Random Signals and Noise","author":"Davenport","year":"1958"},{"key":"10.1016\/S0019-9958(62)90633-2_bib8","first-page":"549","article-title":"Optimum linear filtering of signals prior to sampling","volume":"79","author":"DeRusso","year":"1961","journal-title":"AIEE Trans. II"},{"key":"10.1016\/S0019-9958(62)90633-2_bib9","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TIT.1955.1055126","article-title":"Predictive coding","volume":"IT-1","author":"Elias","year":"1955","journal-title":"IRE Trans. on Information Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib10","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/TIT.1955.1055117","article-title":"A note on the sampling theorem","volume":"IT-1","author":"Fogel","year":"1955","journal-title":"IRE Trans. on Information Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib11","first-page":"179","article-title":"Truncation error of sampling theorem expansions","volume":"50","author":"Helms","year":"1962"},{"key":"10.1016\/S0019-9958(62)90633-2_bib12","first-page":"10","article-title":"Methods of Applied Mathematics","author":"Hildebrand","year":"1952"},{"key":"10.1016\/S0019-9958(62)90633-2_bib13","first-page":"71","article-title":"On the discretization of signals with an unbounded spectrum","volume":"14","author":"Ignat'ev","year":"1960","journal-title":"Elektrosvyaz"},{"key":"10.1016\/S0019-9958(62)90633-2_bib14","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1109\/TIT.1956.1056821","article-title":"Some general aspects of the sampling theorem","volume":"IT-2","author":"Jagerman","year":"1956","journal-title":"IRE Trans. on Information Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib15","first-page":"151","article-title":"Tables of Functions with Formulae and Curves","author":"Jahnke","year":"1945"},{"key":"10.1016\/S0019-9958(62)90633-2_bib16","first-page":"122","article-title":"Discrete representations of random signals","author":"Jordan","year":"1960"},{"key":"10.1016\/S0019-9958(62)90633-2_bib17","series-title":"On the transmission capacity of \u201cether\u201d and wire in electrocommunications","author":"Kotel'nikov","year":"1933"},{"key":"10.1016\/S0019-9958(62)90633-2_bib18","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/S0019-9958(60)90242-4","article-title":"A generalization of the sampling theorem","volume":"3","author":"Linden","year":"1960","journal-title":"Inform. and Control"},{"key":"10.1016\/S0019-9958(62)90633-2_bib19","first-page":"206","article-title":"An Introduction to Statistical Communication Theory","author":"Middleton","year":"1960"},{"key":"10.1016\/S0019-9958(62)90633-2_bib20","first-page":"421","article-title":"Sampling theorem of stationary stochastic variables in multi-dimensional space","volume":"42","author":"Miyakawa","year":"1959","journal-title":"J. Inst. Elec. Commun. Engrs. (Japan)"},{"key":"10.1016\/S0019-9958(62)90633-2_bib21","first-page":"456","article-title":"Methods of Theoretical Physics","author":"Morse","year":"1953"},{"key":"10.1016\/S0019-9958(62)90633-2_bib22","first-page":"617","article-title":"Certain topics in telegraph transmission theory","volume":"47","author":"Nyquist","year":"1928","journal-title":"Trans. AIEE"},{"key":"10.1016\/S0019-9958(62)90633-2_bib23","series-title":"Sampled-Data Control Systems","author":"Ragazzini","year":"1958"},{"key":"10.1016\/S0019-9958(62)90633-2_bib24","series-title":"Application of Miyakawa's multi-dimensional sampling theorem","author":"Sasakawa","year":"1961"},{"key":"10.1016\/S0019-9958(62)90633-2_bib25","first-page":"10","article-title":"Communication in the presence of noise","volume":"37","author":"Shannon","year":"1949"},{"key":"10.1016\/S0019-9958(62)90633-2_bib26","series-title":"The Mathematical Theory of Communication","author":"Shannon","year":"1949"},{"key":"10.1016\/S0019-9958(62)90633-2_bib27","first-page":"43","article-title":"Fourier Transforms","author":"Sneddon","year":"1951"},{"key":"10.1016\/S0019-9958(62)90633-2_bib28","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/TCT.1960.1086679","article-title":"Theoretical bounds on the performance of sampled data communications systems","volume":"CT-7","author":"Spilker","year":"1960","journal-title":"IRE Trans. on Circuit Theory"},{"key":"10.1016\/S0019-9958(62)90633-2_bib29","first-page":"253","article-title":"Statistical design and evaluation of filters for the restoration of sampled data","volume":"44","author":"Stewart","year":"1956"},{"key":"10.1016\/S0019-9958(62)90633-2_bib30","first-page":"181","article-title":"On the functions which are represented by the expansions of the interpolatory theory","volume":"35","author":"Whittaker","year":"1915"},{"key":"10.1016\/S0019-9958(62)90633-2_bib31","first-page":"3","article-title":"The quantization of stochastic signals with infinite spectrum and some results of the theory of pulse transmission of information","volume":"3","author":"Zheleznov","year":"1958","journal-title":"Radiotekh. i Elektron"}],"container-title":["Information and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019995862906332?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019995862906332?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,1,31]],"date-time":"2019-01-31T13:50:50Z","timestamp":1548942650000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0019995862906332"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1962,12]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1962,12]]}},"alternative-id":["S0019995862906332"],"URL":"https:\/\/doi.org\/10.1016\/s0019-9958(62)90633-2","relation":{},"ISSN":["0019-9958"],"issn-type":[{"value":"0019-9958","type":"print"}],"subject":[],"published":{"date-parts":[[1962,12]]}}}