{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T05:46:15Z","timestamp":1791351975691,"version":"4.3.1"},"reference-count":0,"publisher":"Acoustical Society of America (ASA)","issue":"5","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[1978,5,1]]},"abstract":"<jats:p>We present numerical methods for studying the relationship between the shape of the vocal tract and its acoustic output. For a stationary vocal tract, the articulatory-acoustic relationship can be represented as a multidimensional function of a multidimensional argument: y=f(x), where x, y are vectors describing the vocal-tract shape and the resulting acoustic output, respectively. Assuming that y may be computed for any x, we develop a procedure for inverting f(x). Inversion by computer sorting consists of computing y for many values of x and sorting the resulting (y,x) pairs into a convenient order according to y; x for a given y is then obtained by looking up y in the sorted data. Application of this method for determining parameters of an articulatory model corresponding to a given set of formant frequencies is presented. A method is also described for finding articulatory regions (fibers) which map into a single point in the acoustic space. The local nature of f(x) is determined by linearization in a small neighborhood. Larger regions are explored by extending the linear neighborhoods in small steps. This method was applied for the study of compensatory articulation. Sounds produced by various articulations along a fiber were synthesized and were compared by informal listening tests. These tests show that, in many cases of interest, a given sound could be produced by many different vocal-tract shapes.<\/jats:p>","DOI":"10.1121\/1.381848","type":"journal-article","created":{"date-parts":[[2005,10,3]],"date-time":"2005-10-03T22:31:17Z","timestamp":1128378677000},"page":"1535-1555","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":202,"title":["Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique"],"prefix":"10.1121","volume":"63","author":[{"given":"B. S.","family":"Atal","sequence":"first","affiliation":[{"name":"Bell Laboratories, Murray Hill, New Jersey 07974"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. J.","family":"Chang","sequence":"additional","affiliation":[{"name":"Bell Laboratories, Murray Hill, New Jersey 07974"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. V.","family":"Mathews","sequence":"additional","affiliation":[{"name":"Bell Laboratories, Murray Hill, New Jersey 07974"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. W.","family":"Tukey","sequence":"additional","affiliation":[{"name":"Bell Laboratories, Murray Hill, New Jersey 07974"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/63\/5\/1535\/11743320\/1535_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/63\/5\/1535\/11743320\/1535_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T21:53:30Z","timestamp":1689717210000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/63\/5\/1535\/643209\/Inversion-of-articulatory-to-acoustic"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,5,1]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1978,5,1]]}},"URL":"https:\/\/doi.org\/10.1121\/1.381848","relation":{},"ISSN":["0001-4966","1520-8524"],"issn-type":[{"value":"0001-4966","type":"print"},{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1978,5]]},"published":{"date-parts":[[1978,5,1]]}}}