貝蘇章臺灣大學:電信工程學研究所劉宛靈Liu, Wan-LinWan-LinLiu2010-07-012018-07-052010-07-012018-07-052008U0001-2107200815282600http://ntur.lib.ntu.edu.tw//handle/246246/188234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。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。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。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.y 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. e 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.n 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.口試委員會審定書 #謝 #文摘要 #BSTRACT #hapter 1 Introduction 2hapter 2 Lower Triangular Pascal Matrices and Discrete Pascal transform 4.1 Definition 5.1.1 A Description of Pascal’s triangle 5.1.2 Two Types of Pascal matrix – BN and PN 7.1.3 Discrete Pascal Transform 8.2 Properties of Type I and Type II Pascal Matrices 10.2.1 Common properties of lower triangular Pascal matrices 10.2.2 Especial properties of Type II Pascal matrix PN 11.3 Properties of Discrete Pascal Transform 12.3.1 Pascal Transform Pairs 13hapter 3 Unification of Legendre, Laguerre, Hermite, and Binomial discrete transforms using Type I Pascal matrix 16.1 Introduction 16.1.1 Introduction for Discrete Legendre, Laguerre, Hermite, and Binomial Transforms 17.2 Using Type I Pascal Matrix to Unification of Discrete Legendre, Laguerre, Hermite, and Binomial Transforms 20.3 Using Type I Pascal Matrix BN to Form the Discrete Legendre, Laguerre, Hermite, and Binomial Transforms Flow Diagram 22.3.1 To Form the Discrete Laguerre Transform Flow diagram as an Example 24.3.2 To Generalize Transform Flow Diagram 26.4 Summary 26hapter 4 Edge Detection using Discrete Pascal Transform 28.1 Introduction 28.2 Algorithm 30.2.1 Edge Locator by Discrete Pascal Transform 30.2.2 Edge Detection by Discrete Pascal Transform 32.3 Experimental results 33.4 Conclusion 35hapter 5 Interpolation Using Discrete Pascal transform 36.1 Introduction 37.2 Interpolation using Discrete Fourier Transform 38.2.1 Algorithm 38.3 Interpolation by Discrete Pascal Transform 41.3.1 Discrete Pascal Transform Algorithm for Interpolation 41.3.2 Global Interpolation 42.3.3 Local Interpolation by using shifted window 46.4 Experimental Results 48.5 Summary 67hapter 6 Z Transform in Design Digital Filters by Type III Pascal Matrices 68.1 Introduction to transfer functions of filters 69.2 Algorithm 69.2.1 Lowpass Transformation 69.2.2 Transformation from Lowpass to Highpass 73.2.3 Transformation from Lowpass to Bandpass 75.3 Examples 78.4 Summary 84hapter 7 Conclusion and Future works 86.1 Conclusion 86.2 Future Work 88EFERENCE #1058863 bytesapplication/pdfen-US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 triangledigital signal processingdigital image processingedge detectioninterpolationdigital filter designdiscrete Pascal transformthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/188234/1/ntu-97-R95942118-1.pdf