Linear FM Signal Parameter Estimation Using STFT and FRFT

SHEN Liran; YIN Qingbo; LU Mingyu; ZHANG Qi; GUO Lili; SHEN Tianen; ZHAO Guoku; NING Shushi

Article Contents

Article Navigation > Chinese Journal of Electronics > 2013 > 22(2): 301-307

SHEN Liran, YIN Qingbo, LU Mingyu, et al., “Linear FM Signal Parameter Estimation Using STFT and FRFT,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 301-307, 2013,

Citation:

SHEN Liran, YIN Qingbo, LU Mingyu, et al., “Linear FM Signal Parameter Estimation Using STFT and FRFT,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 301-307, 2013,

SHEN Liran, YIN Qingbo, LU Mingyu, et al., “Linear FM Signal Parameter Estimation Using STFT and FRFT,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 301-307, 2013,

Citation:

SHEN Liran, YIN Qingbo, LU Mingyu, et al., “Linear FM Signal Parameter Estimation Using STFT and FRFT,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 301-307, 2013,

PDF( 272 KB)

Linear FM Signal Parameter Estimation Using STFT and FRFT

1.
College of Information Science and Technology, Dalian Maritime University, Dalian 116023, China;
2.
School of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China;
3.
School of Economics and Management, Dalian Ocean University, Dalian 116023, China

Funds: This work is supported by the National Natural Science Foundation of China (No.60803087, No.61073133) and Heilongjiang Postdoctoral Grant (No.LRB08362), and is supported partly by the Fundamental Research Funds for the Central Universities of China (No.2011QN027, No.2011QN126, No.2011ZD010, No.2012TD031), and by Science and Technology Planning Project of Dalian City (No.2011A17GX073, No.2010E15SF153).

Received Date: 2012-02-01
Rev Recd Date: 2012-07-01
Publish Date: 2013-04-25

Abstract

Abstract

A new method, TrTF-FrFT, is introduced for parameter estimation of Linear frequency modulated (LFM) signals, which consists of a coarse search and a fine search. In the initial stage, the window length for Short time Fourier transform (STFT) is selected to get the right time-frequency resolution and concentrate the energy to a line in spectrogram according to the LFM signal characteristic, then the line of ridge energy is tracked in the spectrogram, and the parameters of LFM signal can be estimated coarsely. In the second stage, the fine search for correct parameters is implemented in the Fractional Fourier transform (FRFT) domain using Gaussian model to fit the impulse response of the LFM signals under the guidance from the above stage by the property of monotonicity in the limited neighborhood of the optimal value. In the range of the effective SNR from 20dB to -12dB, the accuracy of the parameter estimation are perfect and affected very little by noise with low computational complexity.
- Linear frequency modulated signal,
- Fractional Fourier transform,
- Parameter estimation,
- Short time Fourier transform

FullText(HTML)

References(34)

References

R.N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. New York: McGraw-Hill, 1978.

J.C. Wood and D.T. Barry, "Radon transformation of timefrequency distributions for analysis of multicomponent signals", IEEE Trans. Signal Process., Vol.42, No.11, pp.3166-3177, 1994.

J.C. Wood and D.T. Barry, "Linear signal synthesis using the Radon-Wigner transform", IEEE Trans. Signal Process., Vol.42, No.8, pp.2105-2111, 1994.

M.S. Wang, A.K. Chan and C.K. Chui, "Linear frequencymodulated signal detection using Radon-ambiguity transform", IEEE Trans. Signal Process., Vol.46, No.3, pp.571-586, 1998.

X.G. Xia, "Discrete chirp-Fourier transform and its application to chirp rate estimation", IEEE Transactions on Signal Processing, Vol.48, No.11, pp.3122-3133, 2000.

S. Mann and S. Haykin, "The chirplet transform: Physical considerations", IEEE Trans. Signal Process., Vol.43, No.11, pp.2745-2761, 1995.

A. Bultan, "A four-parameter atomic decomposition of chirplets", IEEE Trans. Signal Process., Vol.47, No.3, pp.731- 745, 1999.

G. Wang, X. Xia, B. Root, V. Chen, Y. Zhang and M. Amin, "Manoeuvring target detection in over-the-horizon radar using adaptive clutter rejection and adaptive chirplet transform", Inst. Elect. Eng. Proc. Radar Sonar Navig., Vol.150, No.4, pp.292-298, 2003.

Y. Zhang, M. Amin and G. Frazer, "High-resolution timefrequency distributions for manoeuvring target detection in over-the-horizon radars", Inst. Elect. Eng. Proc. Radar Sonar Navig., Vol.150, No.4, pp.299-304, 2003.

S. Barbarossa, "Analysis of multicomponent LFM signals by a combining Wigner-Hough transform", IEEE Trans. Signal Process., Vol.43, No.6, pp.1511-1515, 1995.

Y. Sun and P. Willett, "Hough transform for long Chirp detection", IEEE Trans. Aerosp. Electron. Syst., Vol.38, No.2, pp.553-569, 2002.

L. Cirillo, A. Zoubir, M. Amin, "Parameter estimation for locally linear FM signals using a timefrequency Hough transform", IEEE Transactions on Signal Processing, Vol.56, No.9, pp.4162-4175, 2008.

G. Bi, X. Li and C.Meng, "LFM signal detection using LPPHough transform", Signal Processing, Vol.91, No.6, pp.1432- 1443, 2011.

S. Kay and G. Boudreaux-Bartels, "On the optimality of the Wigner distribution for detection", Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, ICASSP'85, pp.1017-1020, 1985.

W. Li, "Wigner distribution method equivalent to dechirp method for detecting a chirp signal", IEEE Transactions on Acoustics Speech and Signal Processing, Vol.35, No.8, pp.1210- 1211, 1987.

H. Garudadri, "Speech signal analysis using the Wigner distribution", Proceedings of IEEE Pacific Rim Conf. on Communications, Computers and Signal Processing, pp.202-205, 1989.

H. Garudadri, M. Beddoes, A. Benguerel and J. Gilbert, On computing smoothed Wigner distribution, Proceedings of International Conference on Acoustics, Speech, and Signal Processing, ICASSP'87, pp.1521-1524, 1987.

P. Flandrin and O. Rioul, Affine smoothing of the Wigner-Ville distribution, Proceedings of International Conference on Acoustics, Speech, and Signal Processing, ICASSP'90, pp.2455-2458, 1990.

H.M. Ozaktas, Z. Zalevski and M.A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, Wiley, Chichester, UK, 2001.

R. Tao, L. Qin and Y. Wang, Theory and Applications of the Fractional Fourier Transform, Tsinghua University Press, Beijing, China, 2004.

H.M. Ozaktas, M.A. Kutay and G. Bozdagi, "Digital computation of the fractional Fourier transform", IEEE Trans. Sig. Proc., Vol.44, pp.2141-2150, 1996.

B. Adhemar, M.S. Hector, "Computation of the fractional Fourier transform", Applied and Computational Harmonic Analysis, Vol.16, No.3, pp.182-202, 2004.

A. Serbes and L. Durak, "Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains", Communications in Nonlinear Science and Numerical Simulation, Vol.15, No.3, pp.675-689, 2010.

L. Qi, R. Tao, S. Zhou and Y. Wang, "Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform", Science in China. Series F, Vol.47, No.2, pp.184-198, 2004.

R.G. Dorsch, A.W. Lohmann, Y. Bitran, D. Mendlovic and H.M. Ozaktas, "Chirp filtering in the fractional Fourier domain", Applied Optics, Vol.33, No.32, pp.7599-7602, 1994.

Z. Yin and W. Chen, "A new LFM-signal detector based on fractional Fourier Transform", EURASIP Journal on Advances in Signal Processing, Vol.2010, Article ID 876282, 2010.

O. Akay and G.F. Boudreaux-Bartels, "Fractional convolution and correlation via operator methods and an application to detection of linear FM signals", IEEE Transactions on Signal Processing, Vol.49, No.5, pp.979-993, 2001.

L.B. Almeida, "Fractional fourier transform and time frequency representations", IEEE Transactions on Signal Processing, Vol.42, No.11, pp.3084-3091, 1994.

A.W. Lohmann and B.H. Soffer, "Relationships between the Radon-Wigner and fractional Fourier transforms", Journal of the Optical Society of America A, Vol.11, No.6, pp.1798-1801, 1994.

B. Boashash, Interpreting and estimating the instantaneous frequency of a signal-Part I: Fundamentals, Proc. IEEE, Vol.80, pp.519-538, 1992.

L. Griffiths, "Rapid measurement of digital instantaneous frequency", IEEE Trans. Acoust., Speech, Signal Processing, Vol.23, pp.202-221, 1975.

S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory, Englewood Cliffs, NJ: Prentice-Hall, 1998.

R. Groeneveld, G. Meeden, "Measuring skewness and kurtosis", The Statistician, Vol.33, No.4, pp.391-399, 1984.

Howard Anton, Chris Rorres, Elementary Linear Algebra (9th ed.). John Wiley and Sons, Inc., 2005.

Relative Articles

Supplements(0)

Cited By

Proportional views