中央飄移室(CDC)之二維軌跡韌體設計更新是KEK高能加速器機構-國際合作計畫Belle-II 實驗的其中一個項目，我的研究是完成二維軌跡重建之韌體設計，其中包含了2D Finder 和2D Selector。
在2D Finder中我使用了霍夫轉換的技巧將CDC上x-y 平面轉換到霍夫平面，並計算及製作出Track Segment(TS)與霍夫平面上所有格子的對照表，再使用及閘(And gate)套用到所有的SuperLayer上，這過程稱做Hough Voing。在Hough Voting之後，我使用了兩個演算法Pattern-I和Pattern-II來將一群靠近的觸發格子合而為一。並且計算其聚集中心，這過程稱為Clustering。在2D Selector中我將前端(TSF)在每一層SuperLayer送來的20組TS資料轉換到霍夫平面並且和我所選取出的三個最高動量軌跡分別進行比對，找出針對選出的軌跡各自相關的觸發TS，最後必須在每一層SuperLayer中，從所有相關的TS中選出一個符合的相關TS，並將其帶有的資料及在霍夫平面上觸發格子編號送出。
在完成二維軌跡韌體設計之後，我使用了Chipscope軟體去進行除錯，而最後的結果也如同我所預期的。

The updated 2D Tracker Firmware Design for Central Drift Chamber
is the international project related to Belle-II experiment at KEK. My
job is to create the 2D Tracking modules, including 2D Finder and 2D
Selector.
In 2D Finder, I use the skill of Hough transform to transfer the
points in the CDC x-y plane to Hough log(r)- plane. After creating
the Look-Up-Tables for TS to Hough Cells, I use And Logic to all axial
Super Layers. The process is called Hough Voting. After Hough Voting, I use two algorithms named Pattern-I and Pattern-II to combine
the connected Cells into one. And I determine the center of clusters.
This is called Clustering process. In 2D Selector, I translate the 20
TSs into 20 Hough maps and compare with the three selected highest
momentum Hough maps. Finally, one related hit TS in each axial
SuperLayer is selected. The outputs of the 2D Tracker include the
selected TSs information and the ID of the Hough Cells.
After nishing the rmware design, I use the Chipscope software
to debug my rmware code. The results are as expected.

1 Introduction 1
1.1 The Belle and Belle-II Experiment . . . . . . . . . . . 1
1.2 The Central Drift Chamber in Belle and Belle-II . . . . 2
1.3 The Readout Electronics of the CDC . . . . . . . . . . 8
2 The CDC readout electronics: Front-End, Merger and
Track Segment Finder 12
2.1 The main task of CDC . . . . . . . . . . . . . . . . . . 12
2.2 The Front-End of CDC . . . . . . . . . . . . . . . . . . 13
2.3 The Merger of CDC . . . . . . . . . . . . . . . . . . . 14
2.4 The Track Segment Finder of CDC . . . . . . . . . . . 15
3 The 2D Tracking module: 2D Finder 18
3.1 The inputs and outputs of 2D module . . . . . . . . . . 18
3.2 Hough Transform . . . . . . . . . . . . . . . . . . . . . 20
3.3 Hough Voting . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 The 2D Tracking module: 2D Selector 39
4.1 The idea of 2D Selector . . . . . . . . . . . . . . . . . . 39
4.2 The logic of 2D Selector . . . . . . . . . . . . . . . . . 42
4.3 The Firmware algorithm of 2D Selector - Step1 . . . . 43
4.4 The Firmware algorithm of 2D Selector - Step2 . . . . 45
4.5 The Firmware algorithm of 2D Selector - Step3 . . . . 49
4.6 Firmware test by chipscope . . . . . . . . . . . . . . . 50
5 Summary 53

[1] http://legacy.kek.jp/intra-e/index.html
[2] Kobayashi M. and Maskawa T., CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49, 652657,(1973).
[3] http://www.nobelprize.org/
[4] Belle II collaboration, Belle II Technical Design Report, KEK-REPORT-2010-1, July 2010.
[5] http://legacy.kek.jp/intra-e/feature/2010/BelleIICDCDesign.html
[6] http://en.wikipedia.org/wiki/Hough transform
[7] http://belle2.kek.jp/Organization/Belle2CollaborationMap.png
[8] https://belle2.cc.kek.jp/ twiki/pub/Organization/WebHome/BelleII-
Organization.pdf