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研究生： 黃彥桓
Yen-huan Huang
論文名稱： 通訊系統之內插技術研究
指導教授： 薛木添
口試委員:
學位類別： 碩士
Master
系所名稱： 資訊電機學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 中文
論文頁數： 72
中文關鍵詞： 內插法 、插植器 、多項式濾波器
外文關鍵詞： Interpolation technique, Interpolator, Polynomial filter
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    • 通訊系統中，同步資訊傳輸最基本部分之一就是時序恢復。一般來說，接收端是使用固定的取樣頻率，但是由傳送端和接收端的資料取樣時間是不一樣的，這樣會導致非同步的情形發生。所以，在取樣後就必須做內插技術的補償。而內插技術通常是使用多項式去逼近脈衝函數。

    本論文著重在以菲諾架構(Farrow Structure)實現多項式內插法，有升餘弦函數(Raised Cosine Function)、Spline function、Lagrange function、拋物線函數(Parabolic Function)、B-spline function，並分析比較各種多項式函數在同一電路架構上的性能。

    In communication systems, symbol timing recovery is one of the most basic functions. In general, the sampling frequencies of the transmitter and receiver are not the same, this will lead to non-synchronization. Therefore, it is necessary to use interpolation techniques that uses polynomials to approximate the impulse function of ideal low pass filter if the sampling frequency of the receiver is fixed.

    The thesis focuses on the farrow structure achieving polynomials including raised cosine function, spline function, lagrange function, parabolic function, b-spline function. Finally, we analyze and compare the performances of various polynomials in the same structure.

    摘要……………………………………………………………………………………i Abstract…………………………………………………………………………….ii 目錄…………………………………………………………………………………iii 圖目錄…………………………………………………………………………………v 表目錄………………………………………………………………………………vii 第一章 緒論………………………………………………………………………1 1.1 研究動機………………………………………………………………….1 1.2 研究目的………………………………………………………………….4 1.3 論文架構………………………………………………………………….6 第二章 通訊系統簡介……………………………………………………………7 2.1 通訊系統概略…………………………………………………………….7 2.2 同步考量…………………………………………………………………11 2.2.1 符碼同步……………………………………………………………11 2.2.2 載波頻率同步………………………………………………………12 2.2.3 時序同步……………………………………………………………12 第三章 內插法………………………………………………………………….14 3.1 數學模型…………………………………………………………………14 3.2 多項式濾波器……………………………………………………………17 3.2.1 Lagrange interpolation……………………………………………18 3.2.2 Raised cosine function…………………………………………….24 3.2.3 Spline function…………………………………………………….36 3.2.4 Parabolic function…………………………………………………38 3.2.5 B-spline function………………………………………………….39 第四章 模擬結果……………………………………………………………….42 4.1 實驗方法…………………………………………………………………42 4.2 實驗結果…………………………………………………………………43 4.2.1 Raised cosine function…………………………………………….43 4.2.2 Spline function…………………………………………………….49 4.2.3 Lagrange interpolation……………………………………………50 4.2.4 Parabolic function…………………………………………………51 4.2.5 B-spline function………………………………………………….51 4.3 實驗結果分析……………………………………………………………52 第五章 結論及未來展望……………………………………………………….59 參考文獻…………………………………………………………………………….60

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    [10] Hui-Feng Tsai, Zang-Hao Jiang, and Yinyi Lin, “Use of Raised Cosine Interpolator Filter for Timing Recovery,” Journal of the Chinese Institute of Engineers, vol. 34, no. 5, pp. 1-9, July 2011.
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