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dc.contributorJan-Ray Liaoen_US
dc.contributor.authorChi, Hsin-Lanen_US
dc.identifier.citation[1] M. A. Richards, Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005. [2] H. L. V. Trees, Detection, Estimation and Modulation Theory, Part 1. New York: Wiley, 1971. [3] M. D. Macleod, “Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones,” IEEE Transactions on Signal Processing, vol. 46, no. 1, pp. 141–148, 1998. [4] B. G. Quinn, “Estimating frequency by interpolation using Fourier coefficients,” IEEE Transactions on Signal Processing, vol. 42, no. 5, pp. 1264–1268, 1994. [5] B. G. Quinn, “Estimation of frequency, amplitude, and phase from the DFT of a time series,” IEEE Transactions on Signal Processing, vol. 45, no. 3, pp.814–817, 1997. [6] S. Provencher, “Estimation of complex single-tone parameters in the DFT domain,” IEEE Transactions on Signal Processing, vol. 58, no. 7, pp.3879–3883, 2010. [7] E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Processing Magazine, vol. 24, no. 3, pp. 123–125, 2007. [8] C. Candan, “A Method For Fine Resolution Frequency Estimation From Three DFT Samples,” IEEE Signal Processing Letters, vol. 18, no. 6, pp. 351–354, 2011. [9] C. L. Phillips, J. M. Parr, and E. A. Riskin, Signals, Systems, and Transforms, 3rd ed., Pearson Education, 2003. [10] D. E. Knuth, “Johann Faulhaber and sums of powers,” Mathematics of Computation, vol. 61, no. 203, pp. 277–294, 1993. [11] “Discrete-time Fourier Transform,” [12] “Discrete Fourier Transform,” [13] “Taylor series,”泰勒級數. [14] “Bernoulli umbers,”伯努利數. [15] “Cubic function,”
dc.description.abstract  The parameter estimation of complex sinusoidal waveform under white noise usually consists of two stages. The first stage is the coarse search which searches the maximum magnitude in the N-point discrete Fourier transform (DFT) from an input of N samples. The second stage is the fine search which searches around the peak determined in the first stage.   To date, the Candan method is the best method for fine search using DFT coefficient interpolation. It uses three DFT coefficients to achieve high resolution frequency estimation. It is derived from Jacobsen’s estimation equation and added a bias correction term to increase its accuracy. The correction term is effective for the high SNR and adds almost no additional computational cost. Therefore, it can be used in all SNR levels.   This thesis presents three methods that reduce the number of DFT coefficients used in the estimation and three methods that use the same number of samples as in Candan method. In the experiments, the biases and the root mean square (RMS) errors of the six methods are compared with those of Candan method. We show that our methods can be better than Candan method and both the bias and RMS error can be improved significantly.en_US
dc.description.abstract  在白雜訊觀察下複指數波形的參數估測通常為以下兩個階段。第一階段為粗略估測,是應用輸入長度N的N點離散傅立葉轉換(Discrete Fourier Transform,DFT)來搜尋。第二階段為精細搜尋,其搜尋是實施在第一階段決定的峰值附近。   Candan方法為近來最佳的以DFT樣本內差達到精細搜尋的方法。它使用3個DFT樣本處理高解析度頻率估測,推導Jacobsen公式並提出一個偏差校正,這個校正項在高訊號雜訊比(Signal-to-noise ratio,SNR)值是有效的,它幾乎沒有額外的計算成本,所以可以用在任何SNR階層。   本論文提出3種減少DFT樣本數的方法和3種改良3個DFT樣本的方法來做高解析度頻率估測,降低Candan方法所造成的誤差和減少其計算複雜度所造成的影響。最後,我們分析Candan方法與改良方法在不同情況下的偏差與均方根誤差。zh_TW
dc.description.tableofcontents誌謝 i 摘要 ii Abstract iii 目次 iv 圖目次 vi 表目次 vii 第一章 緒論 1   1.1 簡介 1   1.2 動機與目的 1   1.3 論文架構 2 第二章 背景介紹 3   2.1 離散傅立葉轉換(DFT) 3   2.2 從3個DFT樣本高解析度頻率估測 4   2.3 Candan方法之建議估測 6   2.4 Candan方法之流程圖 10   2.5 總結 10 第三章 高解析度頻率估測改良 11   3.1 改良方法之建議估測 11   3.2 減少DFT樣本數之方法 13     3.2.1使用1個DFT樣本之方法1 13     3.2.2使用2個DFT樣本之方法2 13     3.2.3使用2個DFT樣本之方法3 14   3.3 改良3個DFT樣本之方法 14     3.3.1使用3個DFT樣本之方法4 14     3.3.2使用3個DFT樣本之方法5 15     3.3.3使用3個DFT樣本之方法6 15   3.4 改良方法之流程圖 19   3.5 總結 20 第四章 實驗結果與數值比較 21   4.1 軟硬體與比較說明 21   4.2 無雜訊下不同 的偏差 23   4.3 不同SNR下的偏差與均方根誤差 25   4.4 不同 下的偏差與均方根誤差 34   4.6 總結 43 第五章 結論與未來展望 47   5.1 結論 47   5.2 未來展望 47 參考文獻 48zh_TW
dc.subjectFrequency estimationen_US
dc.subjectdiscrete Fourier transformen_US
dc.subjectsignal-to-noise ratioen_US
dc.titleComparison and Improvement for Fine Resolution Frequency Estimation from DFT Samplesen_US
dc.typeThesis and Dissertationzh_TW
item.openairetypeThesis and Dissertation-
item.fulltextno fulltext-
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