{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T02:49:29Z","timestamp":1716950969915},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2008,5,20]],"date-time":"2008-05-20T00:00:00Z","timestamp":1211241600000},"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":[[2008,12]]},"DOI":"10.1007\/s11045-008-0059-y","type":"journal-article","created":{"date-parts":[[2008,5,19]],"date-time":"2008-05-19T16:47:11Z","timestamp":1211215631000},"page":"361-377","source":"Crossref","is-referenced-by-count":1,"title":["Generalized convolution as a tool for the multi-dimensional filtering tasks"],"prefix":"10.1007","volume":"19","author":[{"given":"Przemys\u0142aw","family":"Korohoda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adam","family":"Da\u0327browski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,5,20]]},"reference":[{"issue":"3","key":"59_CR1","first-page":"551","volume":"241","author":"N.N. Aizenberg","year":"1978","unstructured":"Aizenberg N.N. (1978). Spectrum of the convolution of the discrete signals in an arbitrary basis. (In Russian) Proceedings of the USSR Academy of Sciences (Doklady Akademii. Nauk SSSR) 241(3): 551\u2013554","journal-title":"(In Russian) Proceedings of the USSR Academy of Sciences (Doklady Akademii. Nauk SSSR)"},{"key":"59_CR2","unstructured":"Aizenberg, N. N., Aizenberg, I. N., Astola, J., Egiazarian, K. (J. Astola Ed.). (1998). An introduction to algebraic theory of discrete signals. In Proceedings Int. Workshop Transforms and Filter Banks (pp. 70\u201394). Tampere, Finland, Feb. 1998."},{"issue":"11","key":"59_CR3","doi-asserted-by":"crossref","first-page":"4261","DOI":"10.1109\/TSP.2006.881189","volume":"54","author":"I. Aizenberg","year":"2006","unstructured":"Aizenberg I. and Astola J.T. (2006). Discrete generalized Fresnel functions and transform in an arbitrary discrete basis. IEEE Transactions on Signal Processing, 54(11): 4261\u20134270. doi: 10.1109\/TSP.2006.881189","journal-title":"IEEE Transactions on Signal Processing"},{"key":"59_CR4","doi-asserted-by":"crossref","unstructured":"Ahmed, N., & Rao, K. R. (1975). Orthogonal transforms for digital signal processing. Springer.","DOI":"10.1007\/978-3-642-45450-9"},{"issue":"1","key":"59_CR5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1109\/59.486133","volume":"11","author":"H.J. Altuve","year":"1996","unstructured":"Altuve H.J., Diaz I. and Vazquez E. (1996). Fourier and Walsh digital filtering algorithms for distance protection. IEEE Transactions on Power Systems, 11(1): 457\u2013462. doi: 10.1109\/59.486133","journal-title":"IEEE Transactions on Power Systems"},{"key":"59_CR6","unstructured":"Beauchamp, K. G. (1975). Walsh functions and their applications. Academic Press."},{"key":"59_CR7","volume-title":"Digital methods for signal analysis","author":"K.G. Beauchamp","year":"1979","unstructured":"Beauchamp K.G. and Yuen C.K. (1979). Digital methods for signal analysis. George Allen & Unwin, London"},{"key":"59_CR8","unstructured":"Bovik, A. (Ed.). (2000). Handbook of image and video processing. Academic Press."},{"key":"59_CR9","unstructured":"Bracewell, R. N. (2000). The Fourier transform and its applications. McGraw-Hill."},{"key":"59_CR10","volume-title":"Discrete cosine and sine transforms: General properties, fast algorithms and integer approximations","author":"V. Britanak","year":"2007","unstructured":"Britanak V., Yip P.C. and Rao K.R. (2007). Discrete cosine and sine transforms: General properties, fast algorithms and integer approximations. Academic Press, Elsevier"},{"key":"59_CR11","unstructured":"Clarke, R. J. (1985). Transform coding of images. Academic Press."},{"key":"59_CR12","doi-asserted-by":"crossref","unstructured":"Harmuth, H. F. (1972). Transmission of information by orthogonal functions (2nd ed.). Springer.","DOI":"10.1007\/978-3-642-61974-8"},{"key":"59_CR13","unstructured":"Korohoda, P. (2004). Generalized convolution with windowing in the primary domain. In Proceedings of 11th International Workshop on Systems, Signals and Image Processing (IWSSIP\u201904) (pp. 383\u2013386). Pozna\u0144, Sept. 2004."},{"key":"59_CR14","unstructured":"Korohoda, P., & Da\u0327browski, A. (2003). Generalized primary domain interpretation of product filtering of digital signals in the transform domain. In Proceedings of the Signal Processing Workshop (SP 2003) (pp. 75\u201380). Pozna\u0144, Poland, Oct. 2003."},{"key":"59_CR15","unstructured":"Korohoda, P., & Da\u0327browski, A. (2004a). Generalized convolution concept based on DCT. In Proceedings 12th European Signal Processing Conference (EUSIPCO\u201904) (pp. 973\u2013976). Vienna, Austria, Sept. 2004."},{"key":"59_CR16","unstructured":"Korohoda, P., & Da\u0327browski, A. (2004b). Generalized convolution concept for filtering of random signals. In Proceedings of the Signal Processing Workshop (SP 2004) (pp. 55\u201360). Pozna\u0144, Sept. 2004."},{"key":"59_CR17","unstructured":"Korohoda, P., & Da\u0327browski, A. (2005a). Approximation of the generalized convolution\u2014case study example. In Proceedings of the Signal Processing Workshop (SP 2005) (pp. 41\u201344). Pozna\u0144, Sept. 2005."},{"key":"59_CR18","doi-asserted-by":"crossref","unstructured":"Korohoda, P., & Da\u0327browski, A. (2005b). Generalized convolution concept extension to multidimensional signals. In Proceedings of the Fourth International Workshop on Multidimensional Systems (pp. 187\u2013192). Wuppertal, Germany, July 2005.","DOI":"10.1109\/NDS.2005.195352"},{"key":"59_CR19","unstructured":"Korohoda, P., & Da\u0327browski, A. (2006). Generalized convolution for filtering of images in the primary domain. In Proceedings of the Signal Processing Workshop (SP 2006) (pp. 41\u201347). Pozna\u0144, Sept. 2006."},{"key":"59_CR20","doi-asserted-by":"crossref","unstructured":"Korohoda, P., & Da\u0327browski, A. (2007). Fast filtering by generalized convolution related to Discrete Trigonometric Transforms. In Proceedings of the Signal Processing\u2014Algorithms, Architectures, Arrangements and Applications Workshop (SPA 2007) (pp. 57\u201362). Pozna\u0144, Poland, Sept. 2007.","DOI":"10.1109\/SPA.2007.5903300"},{"key":"59_CR21","unstructured":"Madisetti, V. K., & Williams, D. B. (Eds.). (1998). The digital signal processing handbook. CRC Press & IEEE Press."},{"issue":"1","key":"59_CR22","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1190\/1.1444318","volume":"63","author":"G.F. Margrave","year":"1998","unstructured":"Margrave G.F. (1998). Theory of nonstationary linear filtering in the Fourier domain with application to time-variant filtering. Geophysics, 63(1): 244\u2013259. doi: 10.1190\/1.1444318","journal-title":"Geophysics"},{"issue":"5","key":"59_CR23","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1109\/78.295213","volume":"42","author":"S.A. Martucci","year":"1994","unstructured":"Martucci S.A. (1994). Symmetric convolution and the discrete sine and cosine transforms. IEEE Transactions on Signal Processing, 42(5): 1038\u20131051. doi: 10.1109\/78.295213","journal-title":"IEEE Transactions on Signal Processing"},{"key":"59_CR24","unstructured":"Mitra, S. K. (1998). Digital signal processing: A computer based approach. McGraw-Hill."},{"key":"59_CR25","unstructured":"Najarian, K., & Splinter, R. (2006). Biomedical signal and image processing. CRC Press."},{"key":"59_CR26","doi-asserted-by":"crossref","unstructured":"Nussbaumer, H. J. (1982). Fast Fourier transform and convolution algorithms (2nd ed.). Springer.","DOI":"10.1007\/978-3-642-81897-4"},{"key":"59_CR27","doi-asserted-by":"crossref","unstructured":"Poularikas, A. D. (Ed.). (2000). The transforms and applications handbook (2nd ed.). CRC Press & IEEE Press.","DOI":"10.1201\/9781420036756"},{"key":"59_CR28","unstructured":"Proakis, J. G., & Manolakis, D. G. (1996). Digital signal processing: Principles, algorithms and applications (3rd ed.). Prentice Hall."},{"issue":"7","key":"59_CR29","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/LSP.2006.891312","volume":"14","author":"V.G. Reju","year":"2007","unstructured":"Reju V.G., Koh S.N. and Soon I.Y. (2007). Convolution using Dicrete Sine and Cosine Transforms. IEEE Signal Processing Letters, 14(7): 445\u2013448. doi: 10.1109\/LSP.2006.891312","journal-title":"IEEE Signal Processing Letters"},{"key":"59_CR30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1144\/gsjgs.146.1.0133","volume":"146","author":"G.P. Weedon","year":"1989","unstructured":"Weedon G.P. (1989). The detection and illustration of regular sedimentary cycles using Walsh power spectra and filtering, with examples from the Lias of Switzerland. Journal of the Geological Society, 146: 133\u2013144. doi: 10.1144\/gsjgs.146.1.0133","journal-title":"Journal of the Geological Society"},{"key":"59_CR31","doi-asserted-by":"crossref","unstructured":"Yip, P., & Rao, K. R. (1987). Fast discrete transforms. In D. F. Elliott (Ed.), The 6th chapter in: Handbook of digital signal processing. Academic Press.","DOI":"10.1016\/B978-0-08-050780-4.50011-4"}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-008-0059-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-008-0059-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-008-0059-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:34:07Z","timestamp":1559360047000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-008-0059-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,20]]},"references-count":31,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["59"],"URL":"https:\/\/doi.org\/10.1007\/s11045-008-0059-y","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"value":"0923-6082","type":"print"},{"value":"1573-0824","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,20]]}}}