臺灣博碩士論文加值系統

格雷互補序列對具有非週期性自相關函數和為脈衝函數的特性，若使用於非時變線性(LTI)系統的輸入，則可從輸出計算出脈衝響應。本論文使用一階低通濾波器，進行電路模擬測試，並透過MATLAB分析模擬結果，驗證格雷互補對是可應用於類比電路的測試。
因m序列的自相關函數近似於脈衝函數，故也將其應用於一階低通濾波器的電路脈衝響應估測。由模擬測試結果得知，互補序列對比m序列更適合於電路量測。
本論文也對既有文獻 [AS92b] 量測結果進行探討，發現其測試結果並未出現一階電路的指數衰減脈衝響應型態。可能原因為取樣間隔太大，而且使用的PRBS序列自相關函數不佳，不近似脈衝響應。

Golay complementary pair have the property that the sum of aperiodic auto-correlation functions is an impulse function. If it was used in input of LTI, we can calculate an impulse response from LTT’s output. In this thesis, we used 1st-order low pass filter to execute the testing of simulating electrical circuit and use MATLAB to analysis the getting result that we can proof Golay complementary pair can be used for analog circuit testing.
Because the auto-correlation function of m sequence is like the impulse function, it can be used to estimate an impulse response of electrical circuit in 1st-order low pass filter. From the testing result, we know the Golay complementary pair is better than m sequence in surveying electrical circuit.
The thesis is also aim at the testing result of literature [AS92b] to do the research; we find the testing result didn’t have the type of exponential decay impulse response of 1st-order electrical circuit. It maybe the sampling interval is too wide and the auto-correlation function of PRBS sequence is not good, not like impulse response.

中文摘要……………………………………………………………………………….i
英文摘要……………………………………………………………………...……….ii
誌謝…………………………………………………………………………………...iii
目錄…………………………………………………………………………………...iv
表目錄……………………………………………………………………………........v
圖目錄……………………………………………………………………………......vii
第一章 序論…………………………………………………………………………1
1.1 研究背景與目的…………………………………………………………...1
1.2 研究成果…………………………………………………………………...2
1.3 章節提要…………………………………………………………………...3
第二章 研究背景……………………………………………………………………4
2.1 格雷互補序列(Golay complementary sequence, GCS)……...…………4
2.1.1 格雷互補序列的定義………………………………………….…...4
2.1.2 格雷序列的產生方式…….………..……………………………….5
2.2 最大長度序列(Maximum length sequence，簡稱m序列)簡介……..…..6
2.3 系統的簡介…………………………………………….…………….…….6
2.4 以格雷互補對取得離散時間系統脈衝響應…………………….….…….9
第三章 互補序列對應用於電路測試……………………………………………..21
3.1 一階低通濾波器的分析…………………………………….…………….22
3.2 電路模擬………………………………………………..…………………25
3.2.1 實驗設定…………………………………………………………..25
3.2.2 模擬結果…………………………………………….…………….26
3.3 與m序列的比較…………………………………………….…………….36
3.4 既有文獻[AS92b]量測結果探討…………………………………………44
第四章 結論………………………………………………………………………..47
參考文獻…………………………………………………………..……………...….48

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[Gol61] M. J. E. Golay, “Complementary Series,” IRE Trans. On Inform. Theory, vol. IT-7, Issue 2, pp. 82-87, April 1961.
[AS92a] M. A. Al-Qutayri, P. R. Shepherd, “ PRBS Testing Of Analogue Circuits,” IEEE Colloquium On Testing Mixed Signal Circuits, May 1992.
[AS92b] M. A. Al-Qutayri, P. R. Shepherd, “Go/No Go Testing Of Analogue Macros,” IEEE Proceedings G, Vol. 139, No.4 Aug. 1992.
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[DJ99] J. A. Davis, J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2397-2417, Nov. 1999.
[PPT04] M. G. Parker, K. G. Paterson, C. Tellambura, “Golay Complementary Sequences,” Wiley Encyclopedia of Telecommunications, Jan. 2004.
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[CLH08] Chung-Yi Chang , Ying Li, Jonathan Hirata, “More 64-QAM Golay Sequences,” submitted to IEEE Trans. On Inform. Theory, 2008.