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In engineering applications, many measurements of physical quantities can be converted into the problems of frequency estimation. The current frequency estimators are mainly divided into two categories: iterative approaches and direct approaches. However, iterative approaches are not suitable for rapid physical measurement occasions due to its complicated process. But most of the direct approaches are the biased estimators, which are incapable of providing quantitative estimates of variance expression. To enhance the accuracy of the direct frequency estimator and derive the closed-form theoretic expression of the estimated error variance, this paper proposes a novel phase difference frequency estimator based on the forward and backward sub-segmenting. This estimator implements forward and backward fast Fourier transform (FFT) on the given samples separately, and then extracts the phase difference from the peak FFT bins of these two sub-segments to estimate the frequency. And it is emphasized that the proposed method is an unbiased frequency estimator, whose closed-form theoretic expression of the frequency estimated error variance is also derived. Moreover, simulation not only verifies the correctness of this closed-form expression but also proves that the proposed frequency estimator's mean square error is closer to the Cramer-Rao lower bound than that of apFFT/FFT phase difference estimator and Candan estimator. In conclusion, the proposed estimator has higher accuracy in measuring frequencies and has a wide application prospect.
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Keywords:
- frequency estimation /
- forward and backward sub-segment /
- phase difference /
- CRLB
[1] Huang X D, Wang Z H 2008 Journal of Electronics Information Technology 30 293 (in Chinese) [黄翔东, 王兆华 2008 电子与信息学报 30 293]
[2] Candan C 2011 IEEE Signal Processing Letters 18 351
[3] Candan C 2013 IEEE Signal Processing Letters 20 913
[4] Duarte M F, Baraniuk R G 2012 Applied and Computational Harmonic Analysis 1 111
[5] Chen Zh, Zeng Y Ch, Fu Zh J 2008 Acta Phys. Sin. 57 46 (in Chinese) [陈争, 曾以成, 付志坚 2008 57 46]
[6] Cong Ch, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301 (in Chinese) [丛超, 李秀坤, 宋扬 2014 63 064301]
[7] Cheng F, Wang Y Z 2012 Chin. Phys. B 21 070309
[8] Bai Y F, Zhai Sh Q, Gao J R, Zhang J X 2011 Chin. Phys. B 20 034207
[9] Qing H Y, Zhang Y N, Zhou Ch, Zhao Zh Y, Chen G 2014 Acta Phys. Sin. 63 094301 (in Chinese) [青海银, 张援农, 周晨, 赵正予, 陈罡 2014 63 094301]
[10] Zhang Y D, Amin M G, Himed B 2012 EURASIP Journal on Advances in Signal Processing 1 1
[11] Ding Z, Yao X S, Liu T, Du Y, Liu K, Han Q, Meng Zh, Chen H X 2012 Optics Express 20 28319
[12] Stoica P, Moses R L 2005 Spectral analysis of signals (Nanjing: Pearson/Prentice Hall Upper Saddle River)
[13] Liao J R, Chen C M 2014 Signal Processing 94 108
[14] Rife D, Boorstyn R 1974 IEEE Transactions on Information Theory 20 591
[15] Abatzoglou T 1985 IEEE Transactions on Speech and Signal Processing 33 77
[16] Chen K F, Wang J L, Zhang S W 2008 Journal of Vibration Engineering 21 314 (in Chinese) [陈奎孚, 王建立, 张森文2008振动工程学报 21 314]
[17] Ding K, Zhong Sh C 2003 Chinese Journal of Electronics 31 142 (in Chinese) [丁康, 钟舜聪2003电子学报31 142]
[18] Huang X D, Wang Zh H, Luo P, Lv W 2011 Chinese Journal of Electronics 39 172 (in Chinese) [黄翔东, 王兆华, 罗蓬, 吕卫 2011 电子学报 39 172]
[19] Mao Y W, Tu Y Q, Xiao W, Yang H Y 2012 Journal of Vibration and Shock 31 112 (in Chinese) [毛育文, 涂亚庆, 肖玮, 杨辉跃 2012 振动与冲击 31 112]
[20] Tan S W, Ren Zh L, Sun Ch C 2013 Systems Engineering and Electronics 35 34 (in Chinese) [谭思炜, 任志良, 孙常存 2013 系统工程与电子技术 35 34]
[21] Zh X Y, Ding K 2001 Signal Processing. 17 91 (in Chinese) [朱小勇, 丁康 2001 信号处理 17 91]
[22] Quinn B G 1997 IEEE Transactions on Signal Processing 45 814
[23] Mckilliam R G, Quinn B G, Clarkson I V L, Moran B 2010 IEEE Transactions on Signal Processing 58 2953
[24] Macleod M D 1998 IEEE Transactions on Signal Processing 46 141
[25] Deng Zh M, Liu Y 2007 Chinese Journal of Electronics 35 104 (in Chinese) [邓振淼, 刘渝 2007 电子学报 35 104]
[26] Aboutanios E, Mulgrew B 2005 IEEE Transactions on Signal Processing 53 1237
[27] Quinn B G 1994 IEEE Transactions on Signal Processing 42 1264
[28] Provencher S 2010 IEEE Transactions on Signal Processing 58 3879
[29] Ding K, Jiang L Q 2001 Journal of Vibration Engineering 14 354 (in Chinese) [丁康, 江利旗2001振动工程学报 14 354]
[30] Huang X D, Wang Zh H 2008 Journal of Tianjin University 41 815 (in Chinese) [黄翔东, 王兆华2008天津大学学报 41 815]
[31] Qi G Q 2003 Journal of Data Acquisition & Processing 18 7 (in Chinese) [齐国清2003数据采集与处理 18 7]
[32] Zhang T, Ren Zh L, Chen G, Sun Ch C 2011 Systems Engineering and Electronics 33 1468 (in Chinese) [张涛, 任志良, 陈光, 孙常存 2011 系统工程与电子技术 33 1468]
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[1] Huang X D, Wang Z H 2008 Journal of Electronics Information Technology 30 293 (in Chinese) [黄翔东, 王兆华 2008 电子与信息学报 30 293]
[2] Candan C 2011 IEEE Signal Processing Letters 18 351
[3] Candan C 2013 IEEE Signal Processing Letters 20 913
[4] Duarte M F, Baraniuk R G 2012 Applied and Computational Harmonic Analysis 1 111
[5] Chen Zh, Zeng Y Ch, Fu Zh J 2008 Acta Phys. Sin. 57 46 (in Chinese) [陈争, 曾以成, 付志坚 2008 57 46]
[6] Cong Ch, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301 (in Chinese) [丛超, 李秀坤, 宋扬 2014 63 064301]
[7] Cheng F, Wang Y Z 2012 Chin. Phys. B 21 070309
[8] Bai Y F, Zhai Sh Q, Gao J R, Zhang J X 2011 Chin. Phys. B 20 034207
[9] Qing H Y, Zhang Y N, Zhou Ch, Zhao Zh Y, Chen G 2014 Acta Phys. Sin. 63 094301 (in Chinese) [青海银, 张援农, 周晨, 赵正予, 陈罡 2014 63 094301]
[10] Zhang Y D, Amin M G, Himed B 2012 EURASIP Journal on Advances in Signal Processing 1 1
[11] Ding Z, Yao X S, Liu T, Du Y, Liu K, Han Q, Meng Zh, Chen H X 2012 Optics Express 20 28319
[12] Stoica P, Moses R L 2005 Spectral analysis of signals (Nanjing: Pearson/Prentice Hall Upper Saddle River)
[13] Liao J R, Chen C M 2014 Signal Processing 94 108
[14] Rife D, Boorstyn R 1974 IEEE Transactions on Information Theory 20 591
[15] Abatzoglou T 1985 IEEE Transactions on Speech and Signal Processing 33 77
[16] Chen K F, Wang J L, Zhang S W 2008 Journal of Vibration Engineering 21 314 (in Chinese) [陈奎孚, 王建立, 张森文2008振动工程学报 21 314]
[17] Ding K, Zhong Sh C 2003 Chinese Journal of Electronics 31 142 (in Chinese) [丁康, 钟舜聪2003电子学报31 142]
[18] Huang X D, Wang Zh H, Luo P, Lv W 2011 Chinese Journal of Electronics 39 172 (in Chinese) [黄翔东, 王兆华, 罗蓬, 吕卫 2011 电子学报 39 172]
[19] Mao Y W, Tu Y Q, Xiao W, Yang H Y 2012 Journal of Vibration and Shock 31 112 (in Chinese) [毛育文, 涂亚庆, 肖玮, 杨辉跃 2012 振动与冲击 31 112]
[20] Tan S W, Ren Zh L, Sun Ch C 2013 Systems Engineering and Electronics 35 34 (in Chinese) [谭思炜, 任志良, 孙常存 2013 系统工程与电子技术 35 34]
[21] Zh X Y, Ding K 2001 Signal Processing. 17 91 (in Chinese) [朱小勇, 丁康 2001 信号处理 17 91]
[22] Quinn B G 1997 IEEE Transactions on Signal Processing 45 814
[23] Mckilliam R G, Quinn B G, Clarkson I V L, Moran B 2010 IEEE Transactions on Signal Processing 58 2953
[24] Macleod M D 1998 IEEE Transactions on Signal Processing 46 141
[25] Deng Zh M, Liu Y 2007 Chinese Journal of Electronics 35 104 (in Chinese) [邓振淼, 刘渝 2007 电子学报 35 104]
[26] Aboutanios E, Mulgrew B 2005 IEEE Transactions on Signal Processing 53 1237
[27] Quinn B G 1994 IEEE Transactions on Signal Processing 42 1264
[28] Provencher S 2010 IEEE Transactions on Signal Processing 58 3879
[29] Ding K, Jiang L Q 2001 Journal of Vibration Engineering 14 354 (in Chinese) [丁康, 江利旗2001振动工程学报 14 354]
[30] Huang X D, Wang Zh H 2008 Journal of Tianjin University 41 815 (in Chinese) [黄翔东, 王兆华2008天津大学学报 41 815]
[31] Qi G Q 2003 Journal of Data Acquisition & Processing 18 7 (in Chinese) [齐国清2003数据采集与处理 18 7]
[32] Zhang T, Ren Zh L, Chen G, Sun Ch C 2011 Systems Engineering and Electronics 33 1468 (in Chinese) [张涛, 任志良, 陈光, 孙常存 2011 系统工程与电子技术 33 1468]
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