Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/4891
標題: 以離散傅立葉轉換樣本估測高解析度頻率之比較與改良
Comparison and Improvement for Fine Resolution Frequency Estimation from DFT Samples
作者: 紀馨嵐
Chi, Hsin-Lan
關鍵字: 頻率估測
Frequency estimation
離散傅立葉轉換
訊號雜訊比
discrete Fourier transform
signal-to-noise ratio
出版社: 通訊工程研究所
引用: [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,” http://zh.wikipedia.org/zh-hk/DTFT. [12] “Discrete Fourier Transform,” http://zh.wikipedia.org/wiki/DFT. [13] “Taylor series,” http://zh.wikipedia.org/wiki/泰勒級數. [14] “Bernoulli umbers,” http://zh.wikipedia.org/wiki/伯努利數. [15] “Cubic function,” http://en.wikipedia.org/wiki/Cubic_function.
摘要:   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.
  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。
URI: http://hdl.handle.net/11455/4891
其他識別: U0005-0207201211373200
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-0207201211373200
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