{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T16:08:22Z","timestamp":1774022902479,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,19]],"date-time":"2018-09-19T00:00:00Z","timestamp":1537315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministry of Economy and Competitiveness","award":["TEC2016-75067-C4-3-R"],"award-info":[{"award-number":["TEC2016-75067-C4-3-R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.<\/jats:p>","DOI":"10.3390\/e20090719","type":"journal-article","created":{"date-parts":[[2018,9,19]],"date-time":"2018-09-19T10:50:31Z","timestamp":1537354231000},"page":"719","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7423-5505","authenticated-orcid":false,"given":"Jes\u00fas","family":"Guti\u00e9rrez-Guti\u00e9rrez","sequence":"first","affiliation":[{"name":"Tecnun, University of Navarra, Paseo de Manuel Lardiz\u00e1bal 13, 20018 San Sebasti\u00e1n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1866-8004","authenticated-orcid":false,"given":"Marta","family":"Z\u00e1rraga-Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Tecnun, University of Navarra, Paseo de Manuel Lardiz\u00e1bal 13, 20018 San Sebasti\u00e1n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro M.","family":"Crespo","sequence":"additional","affiliation":[{"name":"Tecnun, University of Navarra, Paseo de Manuel Lardiz\u00e1bal 13, 20018 San Sebasti\u00e1n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9628-0681","authenticated-orcid":false,"given":"Xabier","family":"Insausti","sequence":"additional","affiliation":[{"name":"Tecnun, University of Navarra, Paseo de Manuel Lardiz\u00e1bal 13, 20018 San Sebasti\u00e1n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6904","DOI":"10.1109\/TIT.2016.2616139","article-title":"Waterfilling theorems for linear time-varying channels and related nonstationary sources","volume":"62","author":"Hammerich","year":"2016","journal-title":"IEEE Trans. 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