{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T06:35:34Z","timestamp":1718174134993},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,3,26]],"date-time":"2008-03-26T00:00:00Z","timestamp":1206489600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2008,6]]},"DOI":"10.1007\/s00200-008-0077-x","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T13:26:44Z","timestamp":1206451604000},"page":"259-292","source":"Crossref","is-referenced-by-count":3,"title":["Algebraic signal processing theory: Cooley\u2013Tukey type algorithms on the 2-D hexagonal spatial lattice"],"prefix":"10.1007","volume":"19","author":[{"given":"Markus","family":"P\u00fcschel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Rtteler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,3,26]]},"reference":[{"issue":"6","key":"77_CR1","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1109\/TIP.2007.896626","volume":"16","author":"M. P\u00fcschel","year":"2007","unstructured":"P\u00fcschel M. and R\u00f6tteler M. (2007). Algebraic signal processing theory: 2-D hexagonal spatial lattice. IEEE Trans. Image Process. 16(6): 1506\u20131521","journal-title":"IEEE Trans. Image Process."},{"key":"77_CR2","doi-asserted-by":"crossref","unstructured":"P\u00fcschel, M., Moura, J.M.F.: Algebraic signal processing theory: foundation and 1-D time. Part of [3]; IEEE Trans. Signal Process. (2008, to appear)","DOI":"10.1109\/TSP.2008.925261"},{"key":"77_CR3","unstructured":"P\u00fcschel, M., Moura, J.M.F.: Algebraic signal processing theory. Available at http:\/\/arxiv.org\/abs\/cs.IT\/0612077 , parts of this manuscript are submitted as [2,4]"},{"key":"77_CR4","doi-asserted-by":"crossref","unstructured":"P\u00fcschel, M., Moura, J.M.F.: Algebraic signal processing theory: 1-D space. Part of [3]; IEEE Trans. Signal Process. (2008, to appear)","DOI":"10.1109\/TSP.2008.925259"},{"key":"77_CR5","volume-title":"The Chebyshev Polynomials","author":"T.J. Rivlin","year":"1974","unstructured":"Rivlin T.J. (1974). The Chebyshev Polynomials. Wiley Interscience, New York"},{"key":"77_CR6","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/1385-7258(74)90026-2","volume":"36","author":"T. Koornwinder","year":"1974","unstructured":"Koornwinder T. (1974). Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators (part III). Indag. Math. 36: 357\u2013369","journal-title":"Indag. Math."},{"key":"77_CR7","doi-asserted-by":"crossref","unstructured":"P\u00fcschel, M., Moura, J.M.F.: Algebraic signal processing theory: Cooley\u2013Tukey type algorithms for DCTs and DSTs. IEEE Trans. Signal Process. (2008, to appear); a longer version is available at http:\/\/arxiv.org\/abs\/cs.IT\/0702025","DOI":"10.1109\/TSP.2007.907919"},{"issue":"5","key":"77_CR8","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1137\/S009753970139272X","volume":"32","author":"M. P\u00fcschel","year":"2003","unstructured":"P\u00fcschel M. and Moura J.M.F. (2003). The algebraic approach to the discrete cosine and sine transforms and their fast algorithms. SIAM J. Comput. 32(5): 1280\u20131316","journal-title":"SIAM J. Comput."},{"key":"77_CR9","unstructured":"P\u00fcschel, M., R\u00f6tteler, M.: Cooley\u2013Tukey FFT like algorithm for the discrete triangle transform. In: Proceedings of the 11th IEEE DSP Workshop, pp. 158\u2013162 (2004)"},{"issue":"6","key":"77_CR10","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/PROC.1979.11356","volume":"67","author":"R.M. Mersereau","year":"1979","unstructured":"Mersereau R.M. (1979). The processing of hexagonally sampled two-dimensional signals. Proc. IEEE 67(6): 930\u2013949","journal-title":"Proc. IEEE"},{"key":"77_CR11","volume-title":"Multidimensional Digital Signal Processing","author":"D.E. Dudgeon","year":"1984","unstructured":"Dudgeon D.E. and Mersereau R.M. (1984). Multidimensional Digital Signal Processing. Prentice-Hall, Englewood Cliffs"},{"key":"77_CR12","volume-title":"Hexagonal Image Processing","author":"L. Middleton","year":"2005","unstructured":"Middleton L. and Sivaswamy J. (2005). Hexagonal Image Processing. Springer, Heidelberg"},{"issue":"6","key":"77_CR13","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1109\/TSP.2002.1003067","volume":"50","author":"A.M. Grigoryan","year":"2002","unstructured":"Grigoryan A.M. (2002). Hexagonal discrete cosine transform for image coding. IEEE Trans. Signal Process. 50(6): 1438\u20131448","journal-title":"IEEE Trans. Signal Process."},{"key":"77_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-81897-4","volume-title":"Fast Fourier Transformation and Convolution Algorithms","author":"H.J. Nussbaumer","year":"1982","unstructured":"Nussbaumer H.J. (1982). Fast Fourier Transformation and Convolution Algorithms, 2nd edn. Springer, Heidelberg","edition":"2"},{"issue":"193","key":"77_CR15","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1090\/S0025-5718-1991-1052103-1","volume":"56","author":"G. Steidl","year":"1991","unstructured":"Steidl G. and Tasche M. (1991). A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms. Math. Comput. 56(193): 281\u2013296","journal-title":"Math. Comput."},{"key":"77_CR16","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1137\/S0097539792240121","volume":"26","author":"J.R. Driscoll","year":"1997","unstructured":"Driscoll J.R., Healy D.M. Jr. and Rockmore D. (1997). Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs. SIAM J. Comput. 26: 1066\u20131099","journal-title":"SIAM J. Comput."},{"issue":"224","key":"77_CR17","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1090\/S0025-5718-98-00975-2","volume":"67","author":"D. Potts","year":"1998","unstructured":"Potts D., Steidl G. and Tasche M. (1998). Fast algorithms for discrete polynomial transforms. Math. Comput. 67(224): 1577\u20131590","journal-title":"Math. Comput."},{"key":"77_CR18","volume-title":"Representation Theory of Finite Groups","author":"W.C. Curtis","year":"1962","unstructured":"Curtis W.C. and Reiner I. (1962). Representation Theory of Finite Groups. Interscience, New York"},{"key":"77_CR19","unstructured":"Beth, Th.: Verfahren der Schnellen Fouriertransformation [Fast Fourier Transform Methods]. Teubner (1984)"},{"key":"77_CR20","unstructured":"Clausen, M.: Beitr\u00e4ge zum Entwurf schneller Spektraltransformationen (Habilitationsschrift), University of Karlsruhe (1988)"},{"key":"77_CR21","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0304-3975(89)90021-2","volume":"67","author":"M. Clausen","year":"1989","unstructured":"Clausen M. (1989). Fast generalized Fourier transforms. Theor. Comput. Sci. 67: 55\u201363","journal-title":"Theor. Comput. Sci."},{"key":"77_CR22","unstructured":"Clausen, M., Baum, U.: Fast Fourier Transforms. BI-Wiss.-Verl. (1993)"},{"key":"77_CR23","unstructured":"Maslen, D., Rockmore, D.: Generalized FFTs\u2014a survey of some recent results. In: Proceedings of IMACS Workshop in Groups and Computation, vol. 28, pp. 182\u2013238 (1995)"},{"key":"77_CR24","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/0196-8858(90)90008-M","volume":"11","author":"D. Rockmore","year":"1990","unstructured":"Rockmore D. (1990). Fast Fourier analysis for abelian group extensions. Adv. Appl. Math. 11: 164\u2013204","journal-title":"Adv. Appl. Math."},{"key":"77_CR25","doi-asserted-by":"crossref","unstructured":"Maslen, D., Rockmore, D.: Double coset decompositions and computational harmonic analysis on groups. J. Fourier Anal. Appl. 6(4), (2000)","DOI":"10.1007\/BF02510144"},{"key":"77_CR26","unstructured":"Jacobson, N.: Basic Algebra I. W.H. Freeman and Co., San Francisco (1974)"},{"key":"77_CR27","volume-title":"Ideals, Varieties, and Algorithms","author":"D. Cox","year":"1997","unstructured":"Cox D., Little J. and O\u2019Shea D. (1997). Ideals, Varieties, and Algorithms. Springer, Heidelberg"},{"key":"77_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0913-3","volume-title":"Gr\u00f6bner Bases","author":"Th. Becker","year":"1993","unstructured":"Becker Th. and Weispfenning V. (1993). Gr\u00f6bner Bases. Springer, Heidelberg"},{"key":"77_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8734-1","volume-title":"A Polynomial Approach to Linear Algebra","author":"P.A. Fuhrman","year":"1996","unstructured":"Fuhrman P.A. (1996). A Polynomial Approach to Linear Algebra. Springer, New York"},{"key":"77_CR30","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/T-C.1974.223784","volume":"C-23","author":"N. Ahmed","year":"1974","unstructured":"Ahmed N., Natarajan T. and Rao K.R. (1974). Discrete cosine transform. IEEE Trans. Comput. C-23: 90\u201393","journal-title":"IEEE Trans. Comput."},{"key":"77_CR31","doi-asserted-by":"crossref","unstructured":"P\u00fcschel, M., R\u00f6tteler, M.: The discrete triangle transform. Proc. Int. Conf. Acoust. Speech Process., vol. 3, pp. 45\u201348 (2004)","DOI":"10.1109\/ICASSP.2004.1326477"},{"key":"77_CR32","doi-asserted-by":"crossref","unstructured":"Voronenko, Y., P\u00fcschel, M.: Algebraic derivation of general radix Cooley\u2013Tukey algorithms for the real discrete Fourier transform. Proc. Int. Conf. Acoust. Speech Signal Process., vol. 3, pp. 876\u2013879 (2006)","DOI":"10.1109\/ICASSP.2006.1660794"},{"key":"77_CR33","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0196-8858(84)90003-4","volume":"5","author":"L. Auslander","year":"1984","unstructured":"Auslander L., Feig E. and Winograd S. (1984). Abelian semi-simple algebras and algorithms for the discrete Fourier transform. Adv. Appl. Math. 5: 31\u201355","journal-title":"Adv. Appl. Math."},{"issue":"6","key":"77_CR34","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1006\/jsco.2002.0566","volume":"34","author":"M. P\u00fcschel","year":"2002","unstructured":"P\u00fcschel M. (2002). Decomposing monomial representations of solvable groups. J. Symbolic Comput. 34(6): 561\u2013596","journal-title":"J. Symbolic Comput."},{"issue":"9","key":"77_CR35","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1109\/78.942628","volume":"49","author":"S. Egner","year":"2001","unstructured":"Egner S. and P\u00fcschel M. (2001). Automatic generation of fast discrete signal transforms. IEEE Trans. Signal Process. 49(9): 1992\u20132002","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"77_CR36","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jsc.2002.06.005","volume":"37","author":"S. Egner","year":"2004","unstructured":"Egner S. and P\u00fcschel M. (2004). Symmetry-based matrix factorization. J. Symbolic Comput. 37(2): 157\u2013186","journal-title":"J. Symbolic Comput."},{"key":"77_CR37","volume-title":"An Introduction to Orthogonal Polynomials","author":"T.S. Chihara","year":"1978","unstructured":"Chihara T.S. (1978). An Introduction to Orthogonal Polynomials. Gordon and Breach, New York"},{"key":"77_CR38","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF01475757","volume":"260","author":"R. Eier","year":"1982","unstructured":"Eier R. and Lidl R. (1982). A class of orthogonal polynomials in k variables. Math. Ann. 260: 93\u201399","journal-title":"Math. Ann."},{"issue":"4","key":"77_CR39","first-page":"555","volume":"6","author":"P.E. Ricci","year":"1986","unstructured":"Ricci P.E. (1986). An iterative property of Chebyshev polynomials of the first kind in several variables. Rendiconti di Matematica e delle sue Applicazioni 6(4): 555\u2013563","journal-title":"Rendiconti di Matematica e delle sue Applicazioni"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-008-0077-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00200-008-0077-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-008-0077-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T15:24:21Z","timestamp":1558625061000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00200-008-0077-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3,26]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["77"],"URL":"https:\/\/doi.org\/10.1007\/s00200-008-0077-x","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3,26]]}}}