課程名稱 |
近代頻譜分析 Modern Spectral Analysis |
開課學期 |
110-2 |
授課對象 |
電機資訊學院 電機工程學研究所 |
授課教師 |
劉俊麟 |
課號 |
EE5147 |
課程識別碼 |
921 U9640 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四2,3,4(9:10~12:10) |
上課地點 |
明達203 |
備註 |
總人數上限:24人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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課程概述 |
信號處理的重心在於從不同的角度分析訊號。一個常用且重要的方法是分析訊號的頻率成份,或是訊號的頻譜。這個角度在通訊、雷達、陣列信號處理、聲學、影像處理都有其應用。
此課程包含一些分析訊號頻譜的進階方法,主要包含兩個部份。第一部份著重「 recovering the power spectral density of wide-sense stationary random processes」,這部份的頻譜估計方法可分成nonparametric與parametric兩類。第二部份著重近年來的頻譜分析技巧,主題包含sub-Nyquist sampling、compressed sensing、與sparse recovery algorithms。
Part 1: Spectral analysis for WSS random processes
- Signal representation: Random processes
- Nonparametric methods: Periodogram and its extensions
- Parametric methods for line spectra: MUSIC, ESPRIT, etc.
- Performance analysis: Estimation theory, MSE, CRB, etc.
- Applications in array signal processing
Part 2: Spectral analysis with sub-Nyquist sampling and compressed sensing
- Sparse sampling: random sampling, etc.
- Recoverability of sparse vectors: Kruskal's rank, spark, etc.
- Sparse recovery algorithms: \ell_0, matching pursuit, orthogonal matching pursuit, basis pursuit, LASSO, and their extensions
- Performance analysis
- Applications |
課程目標 |
使用近代方法分析訊號之頻譜資訊 |
課程要求 |
此課程為信號處理進階課程,建議修過以下課程(或者有以下關鍵字的背景知識):
線性代數(Linear Algebra ):Orthogonality, eigen-decomposition, Hermitian matrices, norm, dual norm, and matrix norms.
可適性信號處理(Adaptive Signal Processing):Stochastic models (AR, MA, ARMA), Wiener filters, linear prediction, and adaptive beamforming.
凸函數最佳化(Convex Optimization):Convex functions, convex problems, dual problems, and semidefinite programming.
以下課程為選擇性:
偵測與評估(Detection and Estimation Theory):Parameter estimation, (un)biasness, mean-square-error (MSE), and maximum likelihood estimation (MLE). |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
[1] P. Stoica and R. Moses, Spectral Analysis of Signals, Upper Saddle River, N.J. : Pearson/Prentice Hall, 2005.
[2] D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing Spectral Estimation, Signal Modeling, Adaptive Filtering, and Array Processing, Artech House, 2005.
[3] S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, New York, NY : Springer, 2013.
[4] D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques. Addison Wesley Pub. Co. Inc., pp. 1, 1993.
[5] H. L. Van Trees, Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory. Hoboken, NJ, USA: Wiley, 2002.
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評量方式 (僅供參考) |
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