{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,6]],"date-time":"2024-01-06T05:20:36Z","timestamp":1704518436274},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> It has been established that the class of bandpass sigma delta modulators (SDMs) with single bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may also occur in bandpass SDMs with multibit quantizers, even for the case when the saturation regions of the multibit quantizers are not activated and a large number of bits are used for the implementation of the quantizers. Moreover, the fractal pattern may occur for low bit quantizers, and the visual appearance of the phase portraits between the infinite state machine and the finite state machine with high bit quantizers is different. These phenomena are different from those previously reported for the digital filter with two's complement arithmetic. Furthermore, some interesting phenomena are found. A bit change of the quantizer can result in a dramatic change in the fractal patterns. When the trajectories of the corresponding linear systems converge to a fixed point, the regions of the elliptical fractal patterns diminish in size as the number of bits of the quantizers increases. <\/jats:p>","DOI":"10.1142\/s0218127405013976","type":"journal-article","created":{"date-parts":[[2005,12,22]],"date-time":"2005-12-22T05:26:18Z","timestamp":1135229178000},"page":"3377-3380","source":"Crossref","is-referenced-by-count":2,"title":["OCCURRENCE OF ELLIPTICAL FRACTAL PATTERNS IN MULTI-BIT BANDPASS SIGMA DELTA MODULATORS"],"prefix":"10.1142","volume":"15","author":[{"given":"CHARLOTTE YUK-FAN","family":"HO","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BINGO WING-KUEN","family":"LING","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Division of Engineering, King's College London, Strand, London, WC2R 2LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOSHUA D.","family":"REISS","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XINGHUO","family":"YU","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne, VIC 3001, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"7\/1","volume":"23","author":"Feely O.","journal-title":"IEE Colloquium on Oversampling and Sigma-Delta Strategies for DSP"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/31.76495"},{"key":"rf3","first-page":"5188","author":"Lipshitz S. P.","journal-title":"109th Convention of Audio Engineering Society"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/82.559364"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405013976","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:09:18Z","timestamp":1565122158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405013976"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10]]},"references-count":4,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,10]]}},"alternative-id":["10.1142\/S0218127405013976"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405013976","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,10]]}}}