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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 貝蘇章 | |
dc.contributor.author | Wan-Lin Liu | en |
dc.contributor.author | 劉宛靈 | zh_TW |
dc.date.accessioned | 2021-06-13T15:21:39Z | - |
dc.date.available | 2008-07-23 | |
dc.date.copyright | 2008-07-23 | |
dc.date.issued | 2008 | |
dc.date.submitted | 2008-07-23 | |
dc.identifier.citation | [1] R. Brawer and M. Pirovino, The Linear Algebra of the Pascal Matrix, Linear Algebra and Its Application, vol. 174, pp. 13-23, 1992.
[2] Richard A. Haddad, and Thomas W. Parsons, Digital Signal Processing: Theory, Application, and Hardware, New York: CoPuter Science Press, 1991. [3] Weisstein, Eric W, Pascal’s Triangle. From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/PascalsTriangle.html [4] M. F. Aburdene and T. J. Goodman, The Discrete Pascal Transform and Its Applications, IEEE Signal Process. Letters, vol.12, no. 7, July 2005. [5] Q. C. Zhong, A. K. Nandi and M. F. Aburdene, Efficient implementation of Discrete Pascal Transform Using Difference Operators, ELECTRONICS LETTERS, vol.43, no. 24, November 2007 [6] A.N. Skodras, Fast Discrete Pascal Transform, ELECTRONICS LETTERS, vol.42, no. 23, November 2006 [7] T. J. Goodman and M. F. Aburdene, A Hardware Implementation of the Discrete Pascal Transform for Image Processing, Proceedings of SPIE, vol. 6064, January 2006 [8] A.N. Skodras, On the Computation of the Discrete Pascal Transform, Hellenic Open University: Technical Report, HOU-CS-TR-2005-06-EN [9] M. F. Aburdene R. J. Kozick, R. S., Unification of Legendre, Laguerre, Hermite, and Binomial Tansforms Using Pascal Matrix, Multimedia. Syst., Signal Process, vol. 5, pp. 30 t -305, 1994. [10] M. F. Aburdene, R J. Kozick, R.S.Magargle, J. D, Mhney-I-hn, and C. M. Coviello, Discrete Polynomial Transform Representation Using Binary Matrices and Flow Diagrams, in Proc. IEEE Int, Conf. Acoust., Speech, Signal Processing, vol.2, pp.1141-1144, 2001. [11] G. Mandyam and N. Ahmed, The Discrete Laguerre Transform: Derivation and Applications, IEEE Transactions on Signal Processing, vol. 44, pp. 2925-2931, Dec. 1996. [12] Rey-Sern Lin, A Simple Edge Detection Method by Discrete Pascal Transform, in Conf. on AIT, 2007. [13] L. G. Roberts, Machine perception of three-dimensional solids, in Computer Methods in Image Analysis, T. K. Aggarwal, R. O. Duda, and A. Rosenfeld, Eds. Los Angeles: IEEE, 1997. [14] Prewitt and J. M. S., Object Enhancement and Extraction in Picture Processing and Psychopictorics, Lipkin, B. S. and Rosenfeld, A., eds, Academic Press, New York, 1970. [15] J. Canny, A computational approach to edge detection, IEEE Transactions PAMI 8(6), pp.679-698, 1986. [16] D. Marr and E. C. Hildreth, Theory of edge detection, Proc. Roy. Soc. London Ser. B 207, pp.187-217, 1980. [17] M. Petrou and J. Kittler, Optimal Edge Detectors for Ramp Edges, IEEE Transactions PAMI 13(5), pp.483-491, 1991. [18] R. J. Qian and T. S. Huang, Optimal Edge Detectors in Two-Dimensional Images, IEEE Transactions Image Processing 5(7), pp.1215-1220, 1996. [19] J. R. H. Martin and M. Kutter, Information Retrieval in Digital Water Marking, IEEE Commun. Mag. vol. 39, no. 8, pp.110-116, Aug. 2001. [20] B. Li and J. Shen, Rang-image-based Calculation of Three-Dimensional Convex Object Moments, IEEE Transactions Robot. Autom., vol. 9, no. 4, pp. 484-490, 1993. [21] Goodman, T.J., and Aburdene, M.F., Interpolation using the Discrete Pascal Transform, Proc. 2006 Conf. Information Sciences and Systems,Princeton University, NJ, USA, 2006 [22] Ronald W. Schafer and Lawrence R. Rabiner, A Digital Signal Processing Approach to Interpolation, Proceedings of The IEEE, vol. 61, no. 6, June 1973 [23] Rafael C. Gonzalez and Richard E. Woods, Digital Images Processing, 2/E. New Jersey: Prentice Hall, 2002. [24] B. Psenicka, F. Garcia-Ugalde, and A. Herrera-Camacho, The Bilinear Z Transform by Pascal Matrix and Its Application in the Design of Digital Filters, IEEE Signal Process. Lett., vol. 9, no. 11, pp. 368–370, Nov. 2002. [25] B. Psenicka, F. Garcia-Ugalde, and A. Herrera-Camacho, Z Transform from Lowpass to Bandpass by Pascal Matrix, IEEE Signal Process. Lett., vol. 11, no. 2, pp. 282–284, Feb. 2004. [26] T.W. Parks and C. Burrus, Digital Filter Design. New York: Wiley 1987. [27] V. Biolkova and D. Biolek, Generalized Pascal Matrix of first order S-Z transforms, in Poc. ICECS, Pafos, Cyprus, 1999. [28] W Klein, Finite systemtheorie, in Teubner Studienbucher. Stuttgart, Germany: B.G. Teubner, 1976. [29] T. J. Goodman and M. F. Aburdene, On Discrete Pascal Transform, Poisson sequence and Laguerre Polynomials, ELECTRONICS LETTERS, vol. 43, no. 14, July 2007 [30] Bing-Cheng Li and Jun Shen, Pascal transform Approach to the Calculation of 3D Moments, GVGIP, vol. 54, no.4, pp. 301-307, 1992 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37217 | - |
dc.description.abstract | 巴斯卡三角形在數學領域上被研究多年,其擁有許多數學特性。而在這篇論文中,我們將巴斯卡三角形應用於數位訊號處理與影像處理上。
根據巴斯卡三角形,我們定義了兩種巴斯卡下三角矩陣,分別稱為第一類巴斯卡矩陣與第二類巴斯卡矩陣。此外,介紹另一類巴斯卡矩陣,我們稱之為第三類巴斯卡矩陣。其中巴斯卡下三角矩陣是由巴斯卡三角形中的每一列所組合而成的。 在這篇論文中,我們討論這三類巴斯卡矩陣的特性與其在數位訊號處理與影像處理的相關應用,包括統整一些離散轉換,邊緣檢測器,數位訊號的內差法,以及數位濾波器的設計。 值得一提的是,在這篇論文中我們介紹了離散巴斯卡轉換(DPT)。巴斯卡轉換是由Aburdene 和 Goodman所提出。它是屬於離散多項式的轉換,這樣的轉換在訊號處理,影像處理,通訊工程以及系統控制上有很多的應用。我們將會介紹如何利用巴斯卡轉換實現邊緣檢測器以及數位訊號的內差。 | zh_TW |
dc.description.abstract | Pascal triangle was researched by mathematicians ago. It has many mathematical properties. In this article, we apply Pascal triangle in digital signal processing and image processing.
By Pascal triangle, we define two types of the lower triangular Pascal matrices which we denote as type I and type II Pascal matrix respectively, and furthermore introduce a kind of Pascal matrix which we denote as type III Pascal matrix. The lower triangular Pascal matrices, i.e., type I and type II Pascal matrix which we define consist of the rows of Pascal triangle. We discuss three types of Pascal matrices and their relative applications in digital signal processing and image processing, including unification several discrete transforms, edge detection, interpolation, and digital filter design. In particular, we introduce the discrete Pascal transform. The discrete Pascal transform (DPT) was proposed by Aburdene and Goodman. It belongs to the family of the discrete polynomial transforms. Such transform finds numerous applications in signal and image processing, as well as in communication and control systems. We perform how to use the discrete Pascal transform to make an edge detector, and to do interpolations. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T15:21:39Z (GMT). No. of bitstreams: 1 ntu-97-R95942118-1.pdf: 1058863 bytes, checksum: 894103d3644bfb6b5fbc1a3bff57aa2c (MD5) Previous issue date: 2008 | en |
dc.description.tableofcontents | 口試委員會審定書 #
誌謝 # 中文摘要 # ABSTRACT # Chapter 1 Introduction 2 Chapter 2 Lower Triangular Pascal Matrices and Discrete Pascal transform 4 2.1 Definition 5 2.1.1 A Description of Pascal’s triangle 5 2.1.2 Two Types of Pascal matrix – BN and PN 7 2.1.3 Discrete Pascal Transform 8 2.2 Properties of Type I and Type II Pascal Matrices 10 2.2.1 Common properties of lower triangular Pascal matrices 10 2.2.2 Especial properties of Type II Pascal matrix PN 11 2.3 Properties of Discrete Pascal Transform 12 2.3.1 Pascal Transform Pairs 13 Chapter 3 Unification of Legendre, Laguerre, Hermite, and Binomial discrete transforms using Type I Pascal matrix 16 3.1 Introduction 16 3.1.1 Introduction for Discrete Legendre, Laguerre, Hermite, and Binomial Transforms 17 3.2 Using Type I Pascal Matrix to Unification of Discrete Legendre, Laguerre, Hermite, and Binomial Transforms 20 3.3 Using Type I Pascal Matrix BN to Form the Discrete Legendre, Laguerre, Hermite, and Binomial Transforms Flow Diagram 22 3.3.1 To Form the Discrete Laguerre Transform Flow diagram as an Example 24 3.3.2 To Generalize Transform Flow Diagram 26 3.4 Summary 26 Chapter 4 Edge Detection using Discrete Pascal Transform 28 4.1 Introduction 28 4.2 Algorithm 30 4.2.1 Edge Locator by Discrete Pascal Transform 30 4.2.2 Edge Detection by Discrete Pascal Transform 32 4.3 Experimental results 33 4.4 Conclusion 35 Chapter 5 Interpolation Using Discrete Pascal transform 36 5.1 Introduction 37 5.2 Interpolation using Discrete Fourier Transform 38 5.2.1 Algorithm 38 5.3 Interpolation by Discrete Pascal Transform 41 5.3.1 Discrete Pascal Transform Algorithm for Interpolation 41 5.3.2 Global Interpolation 42 5.3.3 Local Interpolation by using shifted window 46 5.4 Experimental Results 48 5.5 Summary 67 Chapter 6 Z Transform in Design Digital Filters by Type III Pascal Matrices 68 6.1 Introduction to transfer functions of filters 69 6.2 Algorithm 69 6.2.1 Lowpass Transformation 69 6.2.2 Transformation from Lowpass to Highpass 73 6.2.3 Transformation from Lowpass to Bandpass 75 6.3 Examples 78 6.4 Summary 84 Chapter 7 Conclusion and Future works 86 7.1 Conclusion 86 7.2 Future Work 88 REFERENCE # | |
dc.language.iso | en | |
dc.title | 巴斯卡矩陣與離散巴斯卡轉換之原理及其應用 | zh_TW |
dc.title | Pascal Matrices and Discrete Pascal Transform: Theory and Related Applications | en |
dc.type | Thesis | |
dc.date.schoolyear | 96-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 李枝宏,馮世邁,丁建均 | |
dc.subject.keyword | 巴斯卡三角形,數位訊號處理,數位影像處理,邊緣檢測,內差法,位濾波器的設計,離散巴斯卡轉換, | zh_TW |
dc.subject.keyword | Pascal triangle,digital signal processing,digital image processing,edge detection,interpolation,digital filter design,discrete Pascal transform, | en |
dc.relation.page | 93 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2008-07-23 | |
dc.contributor.author-college | 電機資訊學院 | zh_TW |
dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
顯示於系所單位: | 電信工程學研究所 |
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