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Title: | 巴斯卡矩陣與離散巴斯卡轉換之原理及其應用 Pascal Matrices and Discrete Pascal Transform: Theory and Related Applications |
Authors: | Wan-Lin Liu 劉宛靈 |
Advisor: | 貝蘇章 |
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, Pascal triangle,digital signal processing,digital image processing,edge detection,interpolation,digital filter design,discrete Pascal transform, |
Publication Year : | 2008 |
Degree: | 碩士 |
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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37217 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 電信工程學研究所 |
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ntu-97-1.pdf Restricted Access | 1.03 MB | Adobe PDF |
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