计及负频率的DFT与DTFT相位差测量误差分析

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摘要针对噪声背景下计及负频率的DFT(Discrete Fourier Transform)与DTFT(Discrete Time Fourier Transform)相位差测量误差问题，用误差理论分别推导出高斯白噪声背景下计及负频率的DFT与DTFT相位差估计方差计算公式。对不同的泄漏误差系数、采样序列长度及信噪比，在负频率影响条件下进行计算验证。结果表明，仿真结果与计算结果一致，表明相位差测量误差分析公式的正确性。提升频率估计精度、增加采样序列长度、提高信号信噪比，可有效提升计及负频率的DFT与DTFT相位差测量方法精度。采样序列长度大于2048点或信噪比大于5 dB时，相位差测量精度提升有限，且DTFT相位差测量方法对频率估计精度更敏感。

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	涂亚庆
	李明
	沈廷鳌
	张海涛

关键词 ：相位差测量, 误差分析, 负频率, DFT, DTFT

Abstract：For the phase difference measurement errors based on DFT(Discrete Fourier Transform) and DTFT (Discrete Time Fourier Transform) methods with negative frequency contribution under white noise background, the formulas for evaluating variance of phase difference measurement DFT and DTFT methods are presented by using error theory. Under the condition of negative frequency contribution, the calculations are carried out for different leakage error coefficients, sampling sequence lengths and signal-noise-ratios (SNR). The simulation results are coinciding with those calculated results using the presented formulas, which show the correctness of the phase measurement error analysis formula. The accuracy of DFT and DTFT based phase difference measurement methods with negative frequency contribution could be improved effectively by enhancing the frequency estimation accuracy, increasing the sampling sequence length, and improving the SNR. When the sampling sequence length is more than 2048 or SNR is greater than 5dB, the accuracy of phase difference measurement is improved limited. The DTFT based phase measurement method is more sensitive to frequency estimation accuracy.

Key words： phase difference measurement error analysis negative frequency discrete fourier transform (DFT) discrete time fourier transform (DTFT)

收稿日期: 2014-01-08 出版日期: 2015-10-25

引用本文:

涂亚庆，李明，沈廷鳌，张海涛 . 计及负频率的DFT与DTFT相位差测量误差分析[J]. 振动与冲击, 2015, 34(20): 85-91.
TU Ya-qing，LI Ming，SHEN Ting-ao，ZHANG Hai-tao. Error analysis of DFT and DTFT based phase difference measurement with negative frequency contribution. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(20): 85-91.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I20/85

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