# 臺灣博碩士論文加值系統

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 在有雜訊的情況下，阻尼弦波信號的參數估測，在很多地方都有非常重要的應用，像是雷達、聲納等等。其可在時間域中或頻率域中估測，而時間域估測的演算法，缺點是計算複雜度相對較高；而在頻率域估測的優點，便是其頻譜的能量集中，計算較簡單。 故本篇論文，探討的是在頻域中做參數估測，一開始會先介紹Bertocco和Petri共同提出在有阻尼情況下的演算法，其演算法在於找到做了傅立葉轉換後，所得的轉換係數最大絕對值，並利用其鄰近的兩個點做比較，選擇較大值，來與最大絕對值做參數估測，但此演算法離估測的理想極限Cramer-Rao Lower Bound(CRLB)，仍有段距離，表示誤差仍具有修正空間，故便針對其估測演算法做改進，實現了Qian的估測演算法，同理找出轉換係數的最大絕對值，但會將最大絕對值與鄰近的兩個點分別加以計算，求出兩個解，並使用了一維高斯牛頓法，尋找將兩個解合併的最佳組合，以達到較佳的估測結果。
 Damped sinusoidal signal estimation under noise has many applications such as radar and sonar signal processing. It can be done in either time domain or frequency domain. The estimation algorithms in time domain are more complex and have high computational cost. On the other hand, the energy in frequency domain is more concentrated around the sinusoidal frequency and the estimation in frequency domain is much simpler than the estimation in time domain.This thesis discusses the damped sinusoidal signal estimation in frequency domain. We first introduce the algorithm proposed by Bertocco and Petri. The algorithm finds the maximum coefficient of the discrete Fourier transform (DFT) and uses the larger one of the two neighboring coefficients to estimate the parameters of the damped sinusoids. However, the Bertocco and Petri algorithm still has some distance toward the ideal Cramer-Rao lower bound (CRLB). This thesis implements the algorithm proposed by Qian. The Qian algorithm uses the maximum of the DFT coefficients and both of the two neighboring coefficients to obtain two solutions. It then uses Newton-Gauss algorithm to find the optimal combination of the two solutions. Experiments show that the Qian algorithm is much better than Bertocco and Petri algorithm.
 目錄誌謝 I摘要 IIAbstract III目錄 IV圖目錄 V第一章 緒論 11.1簡介 11.2論文架構 1第二章 文獻回顧 22.1 Bertocco和Petri演算法 2第三章 參數估測演算法的改良 53.1 Qian演算法 5第四章 實驗結果與輸出 124.1模擬環境 124.2實驗結果與輸出 12第五章 結論 225.1結論 22參考文獻 23
 參考文獻[1] S. M. Kay, Modern Spectral Estimation, Prentice-Hall, NJ, 1988.[2] R. Kumaresan, D.W. Tufts,” Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise,” IEEE Trans. Acoust. Speech Signal Process., vol.30, pp.833–840, 1982.[3] B. Porat, B. Friedlander, “A modification of the Kumaresan–Tufts method for estimating rational impulse responses,” IEEE Trans. Acoust. Speech Signal Process., vol.34, pp.1336–1338, 1986.[4] Y. Li, K.J.R. Liu, J. Razavilar, “A parameter estimation scheme for damped sinusoidal signals based on low-rank Hankel approximation,” IEEE Trans. Signal Process., vol.45, pp.481–486, 1997.[5] Y. Hua, T.K. Sarkar, “Matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise,” IEEE Trans. Acoust. Speech Signal Process., vol.38, pp.814–824, 1990.[6] S. Minhas, E. Aboutanios, “Estimation of the frequency of a complex exponential,” in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3693–3696, 2008.[7] S. Reisenfeld, E. Aboutanios, “A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise,” IEEE Commun. Lett., vol.7, pp.549–551, 2003.[8] C.O.M. Bertocco, D. Petri, “Analysis of damped sinusoidal signals via a frequency-domain interpolation algorithm,” IEEE Trans. Instrum. Meas, vol.43, pp.245–250, 1994.[9] F. Qian, S. Leung, Y. Zhu,” Damped sinusoidal signals parameter estimation in frequency domain,” Signal Process., vol.92, pp.381–391, 2012.
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