Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples

XIANG Jinzhi; CUI Wei; SHEN Qing

doi:10.1049/cje.2017.09.019

Volume 27 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Electronics > 2018 > 27(1): 109-114

XIANG Jinzhi, CUI Wei, SHEN Qing, “Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples,” Chinese Journal of Electronics, vol. 27, no. 1, pp. 109-114, 2018, doi: 10.1049/cje.2017.09.019

Citation:

XIANG Jinzhi, CUI Wei, SHEN Qing, “Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples,” Chinese Journal of Electronics, vol. 27, no. 1, pp. 109-114, 2018, doi: 10.1049/cje.2017.09.019

Citation:

PDF( 1824 KB)

Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples

doi: 10.1049/cje.2017.09.019

School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61672097).

More Information

Corresponding author: CUI Wei (corresponding author) was born in Inner Mongolia Autonomous region, China, in 1976. He received the B.S. degree in physics and Ph.D. degree in Electronics Engineering from Beijing Institute of Technology, Beijing, China, in 1998 and 2003, respectively.. (Email:cuiwei@bit.edu.cn)
Received Date: 2017-01-16
Rev Recd Date: 2017-05-03
Publish Date: 2018-01-10

Abstract

Abstract

A flexible and accurate frequency estimator is first proposed for frequency estimation of a complex sinusoid weighted with a rectangular window function in additive white Gaussian noise. This proposed frequency estimator can be operated in the application of an arbitrary length discrete Fourier transform where the original input data is padded with any zeroes, which makes it more flexible in practice. The proposed frequency estimator utilizes the maximum sample value and its two adjacent samples in the frequency domain to perform the fine frequency estimation with unbiased results obtained. Then a modified frequency estimator is proposed to estimate the frequency when the complex sinusoid signal is weighted with different nonrectangular window functions. Although the modified frequency estimator is nonanalytic and biased, it can still improve the estimation performance for certain applications. Simulation results demonstrate that both of the proposed frequency estimators are effective to achieve the high frequency estimation accuracy. And the root mean square errors of the proposed frequency estimators approach the Cramer-Rao bound when the signal-to-noise ratio is large enough to make the coarse frequency estimation work effectively.
- Frequency estimation,
- Complex sinusoid,
- DFT interpolation,
- Zero-padding

FullText(HTML)

References(19)

References

D.C. Rife and R.R. Boorstyn, "Single tone parameter estimation from discrete-time observations", IEEE Trans. Inf. Theory, Vol.20, No.5, pp.591-598, 1974.

B.G. Quinn, "Estimating frequency by interpolation using Fourier coefficients", IEEE Trans. Signal Process, Vol.42, No.5, pp.1265-1268, 1994.

B.G. Quinn, "Estimation of frequency, amplitude and phase from the DFT of a time series", IEEE Trans. Signal Process, Vol.45, No.3, pp.814-817, 1997.

B.G. Quinn, " Recent advances in rapid frequency estimation", Digital Signal Process, Vol.19, No.6, pp.942-948, 2009.

W. Cui, S. Wu, J. Tian, D.C. Liu and S.L. Wu, "Parameter estimation for maneuvering targets with complex motion via scaled double-autocorrelation transform", Digital Signal Process, Vol.59, No.2, pp.31-48, 2016.

M.D. Macleod, "Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones", IEEE Trans. Signal Process, Vol.46, No.1, pp.141-148, 1998.

E. Jacobsen and P. Kootsookos, "Fast, accurate frequency estimators", IEEE Signal Process Mag., Vol.24, No.3, pp.123-125, 2007.

C. Candan, "A method for fine resolution frequency estimation from three DFT samples", IEEE Signal Process Lett., Vol.18, No.6, pp.351-354,2011.

C. Candan, "Analysis and further improvement of fine resolution frequency estimation method from three DFT samples", IEEE Signal Process Lett., Vol.20, No.9, pp.913-916, 2013.

J.R. Liao and S. Lo, "Analytical solutions for frequency estimators by interpolation of DFT coefficients", Signal Process, Vol.100, No.7, pp.93-100, 2014.

J. Tian, W. Cui, X.L. Lv, S. Wu and S.L. Wu, "Parameter estimation of maneuvering targets based on segment integration and Lv's transform", IET Radar, Sonar & Navigation, Vol.9, No.5, pp.600-607, 2015.

S. Reisenfeld and E. Aboutanios, "A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise", IEEE Commun. Lett., Vol.7, No.11, pp.549-551, 2003.

E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients", IEEE Trans. Signal Process, Vol.53, No.4, pp.1237-1242, 2005.

Y.H. Liu, Z.P. Nie and Z.Q. Zhao, "An iterative frequency estimation algorithm using generalized Fourier interpolation", Chinese Journal of Electronics, Vol.18, No.2, pp.565-568, 2009.

X.D. Wang, T. Fan, Q.H. Huang and B.S. Zheng, "SOQPSK carrier tracking technology with large doppler frequency offset based on FFT guided costas loop", Acta Electronica Sinica, Vol.44, No.2, pp.491-496, 2016. (in Chinese)

J. Tian, W. Cui and S.L. Wu, "A novel method for parameter estimation of space moving targets", IEEE Geoscience and Remote Sensing Lett.,Vol.11, No.2, pp.389-393, 2014.

Y.T. Wu, L.T. Huang, H. Cao and Y.B. Zhang, "HOSVD-based subspace algorithm for multidimensional frequency estimation without pairing parameters", Chinese Journal of Electronics, Vol.23, No.4, pp.729-734, 2014.

C. Yang and G. We, "A noniterative frequency estimator with rational combination of three spectrum lines", IEEE Trans. Signal Process, Vol.59, No.10, pp.5065-5070, 2011.

X.H. Liang, A.J. Liu, X.F. Pan, Q.S. Zhang and F. Chen, "A new and accurate estimator with analytical expression for frequency estimation", IEEE Commun. Lett., Vol.20, No.1, pp.105-108, 2016.

Relative Articles

Supplements(0)

Cited By

Proportional views