{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T15:40:22Z","timestamp":1684424422169},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,5,30]],"date-time":"2008-05-30T00:00:00Z","timestamp":1212105600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multidim Syst Sign Process"],"published-print":{"date-parts":[[2009,3]]},"DOI":"10.1007\/s11045-008-0060-5","type":"journal-article","created":{"date-parts":[[2008,5,29]],"date-time":"2008-05-29T16:46:11Z","timestamp":1212079571000},"page":"3-24","source":"Crossref","is-referenced-by-count":7,"title":["Multidimensional perfect reconstruction filter banks: an approach of algebraic geometry"],"prefix":"10.1007","volume":"20","author":[{"given":"Lei","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anamitra","family":"Makur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,5,30]]},"reference":[{"key":"60_CR1","unstructured":"Adams, W. W., & Loustaunau, P. (1996). An introduction to Gr\u00f6bner bases. Providence, R.I.: American Mathematical Society."},{"issue":"8","key":"60_CR2","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1016\/S0016-0032(98)00006-4","volume":"335","author":"S. Basu","year":"1998","unstructured":"Basu S. (1998) Multi-dimensional filter banks and wavelets\u2014a system theoretic perspective. Journal of the Franklin Institute 335(8): 1367\u20131409","journal-title":"Journal of the Franklin Institute"},{"issue":"12","key":"60_CR3","doi-asserted-by":"crossref","first-page":"3256","DOI":"10.1109\/78.735301","volume":"46","author":"H. Bolcskei","year":"1998","unstructured":"Bolcskei H., Hlawatsch F., Feichtinger H.G. (1998) Frame-theoretic analysis of oversampled filter banks. IEEE Transactions on Signal Processing 46(12): 3256\u20133268","journal-title":"IEEE Transactions on Signal Processing"},{"key":"60_CR4","unstructured":"Bose, N. K. (2003). Multidimensional Systems Theory and Applications. Kluwer Academic Publishers."},{"key":"60_CR5","unstructured":"Bunchberger, B. (1965). An algorithm for finding the bases elements of the residue class ring modulo a zero dimensional polynomial ideal. Ph.D thesis, University of Innsbruck."},{"issue":"12","key":"60_CR6","doi-asserted-by":"crossref","first-page":"1475","DOI":"10.1109\/82.809533","volume":"46","author":"C. Charoenlarpnopparut","year":"1999","unstructured":"Charoenlarpnopparut C., Bose N.K. (1999) Multidimensional FIR filter bank design using Gr\u00f6bner bases. IEEE Transactions on Circuits and Systems II: Express Briefs 46(12): 1475\u20131486","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"issue":"3\u20134","key":"60_CR7","first-page":"345","volume":"12","author":"C. Charoenlarpnopparut","year":"2001","unstructured":"Charoenlarpnopparut C., Bose N.K. (2001) Gr\u00f6bner bases for problem solving in multidimensional systems. Multidimensional Systems and Signal Processing archive 12(3\u20134): 345\u2013364","journal-title":"Multidimensional Systems and Signal Processing archive"},{"issue":"2","key":"60_CR8","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/76.212718","volume":"3","author":"T. Chen","year":"1993","unstructured":"Chen T., Vaidyanathan P.P. (1993) Recent developments in multidimensional multirate systems. IEEE Transactions on Circuits and Systems for Video Technology 3(2): 116\u2013137","journal-title":"IEEE Transactions on Circuits and Systems for Video Technology"},{"key":"60_CR9","unstructured":"Cox, D., Little, J., & O\u2019Shea, D. (1996). Ideals, varieties, and algorithms (2nd ed.). Springer-Verlag New York Inc."},{"key":"60_CR10","doi-asserted-by":"crossref","unstructured":"Galkowski, K. (Ed.). (2001). Multidimensional signals, circuits and systems. Taylor and Francis.","DOI":"10.1201\/b12585"},{"key":"60_CR11","unstructured":"Greuel, G. M., Pfister, G., & Sch\u00f6nemann, H. (2005). \u201cSingular 3.0.\u201d A computer algebra system for polynomial computations, centre for computer algebra, University of Kaiserslautern. http:\/\/www.singular.uni-kl.de ."},{"key":"60_CR12","first-page":"2121","volume":"4","author":"T. Kalker","year":"1995","unstructured":"Kalker T., Park H., Vetterli M. (1995) Groebner basis techniques in multidimensional multirate systems. Proceeding, ICASSP 4: 2121\u20132124","journal-title":"Proceeding, ICASSP"},{"issue":"6","key":"60_CR13","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/29.56054","volume":"38","author":"G. Karlsson","year":"1990","unstructured":"Karlsson G., Vetterli M. (1990) Theory of Two-dimensional Multirate Filter Banks. IEEE Transactions on ASSP 38(6): 925\u2013937","journal-title":"IEEE Transactions on ASSP"},{"issue":"5","key":"60_CR14","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1109\/78.382414","volume":"43","author":"J. Kovacevic","year":"1995","unstructured":"Kovacevic J., Vetterli M. (1995) Nonseparable two- and three-dimensional wavelets. IEEE Transactions on Signal Processing 43(5): 1269\u20131273","journal-title":"IEEE Transactions on Signal Processing"},{"key":"60_CR15","first-page":"505","volume":"2","author":"K. Kurosawa","year":"1994","unstructured":"Kurosawa K. (1994) On McClellan transform and 2-D QMF banks. Proceeding, ISCAS 2: 505\u2013508","journal-title":"Proceeding, ISCAS"},{"key":"60_CR16","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.laa.2004.01.008","volume":"391","author":"Z. Lin","year":"2004","unstructured":"Lin Z., Xu L., Wu Q. (2004) Appliation of Gr\u00f6bner bases to signals and image processing: A survey. Linear algebra and its application 391: 169\u2013202","journal-title":"Linear algebra and its application"},{"issue":"1","key":"60_CR17","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TCSI.2007.914007","volume":"55","author":"Z. Lin","year":"2008","unstructured":"Lin Z., Xu L., Bose N.K. (2008) A tutorial on Gr\u00f6bner bases with applications in signals and systems (Invited paper). IEEE Transactions on Circuits and Systems I 55(1): 445\u2013461","journal-title":"IEEE Transactions on Circuits and Systems I"},{"issue":"3\u20134","key":"60_CR18","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01826246","volume":"7","author":"Y.P. Lin","year":"1996","unstructured":"Lin Y.P., Vaidyanathan P.P. (1996) Theory and design of two-dimensional filter banks: A review. Multidimensional Systems and Signal Processing 7(3\u20134): 263\u2013330","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"60_CR19","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1109\/TCS.1976.1084236","volume":"CAS-23","author":"R.M. Mersereau","year":"1976","unstructured":"Mersereau R.M., Mecklenbrauker W.F.G., Quatieri T.F. Jr. (1976) McClellan transformations for two-dimensional digital filtering, I: Design. IEEE Transactions on Circuits and Systems CAS-23: 405\u2013414","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"5","key":"60_CR20","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1109\/29.17560","volume":"37","author":"T.Q. Nguyen","year":"1989","unstructured":"Nguyen T.Q., Vaidyanathan P.P. (1989) Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Transactions on ASSP 37(5): 676\u2013690","journal-title":"IEEE Transactions on ASSP"},{"issue":"3\u20134","key":"60_CR21","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1011961708408","volume":"12","author":"H. Park","year":"2001","unstructured":"Park H. (2001) Parametrized family of 2-D non-factorable FIR lossless systems and Gr\u00f6bner bases. Multidimensional Systems and Signal Processing 12(3\u20134): 345\u2013364","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"6","key":"60_CR22","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1109\/TCSI.2002.1010039","volume":"49","author":"H. Park","year":"2002","unstructured":"Park H. (2002) Optimal design of synthesis filters in multidimensional perfectreconstruction FIR filter banks using Grobner bases. IEEE Transactions on Circuits and Systems I: Regular Papers 49(6): 843\u2013851","journal-title":"IEEE Transactions on Circuits and Systems I: Regular Papers"},{"issue":"1\u20132","key":"60_CR23","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1023\/A:1008299221759","volume":"8","author":"H. Park","year":"1997","unstructured":"Park H., Kalker T., Vetterli M. (1997) Gr\u00f6bner bases and multidimensional FIR multirate systems. Multidimensional Systems and Signal Processing 8(1\u20132): 11\u201330","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"60_CR24","volume-title":"Multirate systems and filter banks","author":"P.P. Vaidyanathan","year":"1993","unstructured":"Vaidyanathan P.P. (1993) Multirate systems and filter banks. Englewood Cliffs, Prentice Hall"},{"issue":"1","key":"60_CR25","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/31.101301","volume":"38","author":"E. Viscito","year":"1991","unstructured":"Viscito E., Allebach J.P. (1991) The analysis and design of multidimensional FIR perfectreconstruction filter banks for arbitrary sampling lattices. IEEE Transactions on Circuits and Systems 38(1): 29\u201341","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"10","key":"60_CR26","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1109\/97.633773","volume":"4","author":"D. Wei","year":"1997","unstructured":"Wei D., Evans B.L., Bovik A.C. (1997) Loss of perfect reconstruction in multidimensional filterbanks and wavelets designed via extended McClellan transformations. IEEE Singal Processing Letter 4(10): 295\u2013297","journal-title":"IEEE Singal Processing Letter"},{"key":"60_CR27","first-page":"609","volume":"4","author":"L. Zhang","year":"2005","unstructured":"Zhang L., Makur A. (2005) Structurally linear phase factorization of 2-channel filter banks based on lifting. Proceeding, ICASSP 4: 609\u2013612","journal-title":"Proceeding, ICASSP"},{"issue":"7","key":"60_CR28","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.jfranklin.2006.05.003","volume":"343","author":"L. Zhang","year":"2006","unstructured":"Zhang L., Makur A. (2006) Comments on \u2018multi-dimensional filter banks and wavelets-A system theoretic perspective\u2019. Journal of the Franklin Institute 343(7): 699\u2013704","journal-title":"Journal of the Franklin Institute"},{"key":"60_CR29","doi-asserted-by":"crossref","unstructured":"Zhang, L., & Makur, A. (2005). Structurally linear phase factorization of 2-channel filter banks based on lifting. Proceeding, ICASSP, 4, 609\u2013612.","DOI":"10.1109\/ICASSP.2005.1416082"},{"issue":"10","key":"60_CR30","doi-asserted-by":"crossref","first-page":"2998","DOI":"10.1109\/TIP.2006.877487","volume":"15","author":"J. Zhou","year":"2006","unstructured":"Zhou J., Do M.N. (2006) Multidimensional multichannel FIR deconvolution using Gr\u00f6bner bases. IEEE. Transactions on Image Processing 15(10): 2998\u20133007","journal-title":"IEEE. Transactions on Image Processing"}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-008-0060-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-008-0060-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-008-0060-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T15:08:22Z","timestamp":1684422502000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-008-0060-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,30]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["60"],"URL":"https:\/\/doi.org\/10.1007\/s11045-008-0060-5","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"value":"0923-6082","type":"print"},{"value":"1573-0824","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,30]]}}}