Investigating Bias of DCFT, DPT and Promoted DPT Methods in terms of Phase Parameters Estimation of Chirp Signal

Rabiee, Nooshin; Aazad, Hamid; Parhizgar, Naser

doi:10.52547/mjee.15.3.35

Document Type : Review Article

Authors

¹ Department of Electrical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

² Department of Electrical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

https://doi.org/10.52547/mjee.15.3.35

Abstract

Amongst the approaches proposed to estimate parameters of a chirp signal sequentially, i.e., the central frequency and the chirp rate, algorithms, such as discrete polynomial-phase transform (DPT) and promoted DPT, exhibit acceptable estimation accuracy. Algorithms intended to estimate phase parameters sequentially, diminish the order of polynomials in complex exponential power to lower-order polynomials, and then estimate these two parameters using the NLS method in a given single exponential mode. The NLS method, which uses FFT to decrease the computational load of frequency domain search, encounters predicaments. In this work, we assessed the bias of algorithms intended for estimating of phase parameters sequentially using the RBF method. The results of investigating the bias of estimators indicated the improved accuracy of the DPT and promoted DPT algorithms in estimation using the RBF method instead of NLS and also than DCFT method.

Keywords

References

[1] S. Chatterjee, S. Dalai, S. Chakravorti, B. Chatterjee , “Use of chirp excitations for frequency domain spectroscopy measurement of oil-paper insulation,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 25 ,Issue. 3, pp. 1103 – 1111, June 2018.

[2] S. Sankar Dhar, D. Kundu , Ujjwal Das, “Tests For the Parameters of Chirp Signal Model,” IEEE Transactions on Signal Processing, Vol. 67, Issue. 16, pp. 4291 – 4301, Aug 2019.

[3] Peleg S. Friedlander B, “The discrete polynomial–phase transform,” IEEE Transactions on Signal Processing, Vol. 43, No. 8, pp. 1901–1914, 1995

[4] Perry RP. DiPietro RC. Fante R, “SAR imaging of moving targets,”IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 1, pp. 188–200, 1999.

[5] Rankine N. Stevenson M. Mesbah M. Boashash B, “A nonstationary model of newborn EEG,” IEEE Transactions on Biomedical Engineering, Vol. 54, No. 1, pp. 19–28, 2007.

[6] Vespe M. Jones G. Baker C, “Lessons for radar: waveform diversity inecholocating mammals,”IEEE Signal Processing Magazine, Vol. 26, No. 1, pp. 65–75, 2009.

[7] Abatzoglou T J, “Fast maximum likelihood joint estimation of frequency and frequency rate,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 22, No. 6, pp.708–715, 1986.

[8] Volcker B. Ottersten B, “Chirp parameter estimation using rank reduction. Conference Record of Thirty–Second Asilomar Conference on Signals,”Systems and Computers, Pacific Grove, CA, USA, pp. 1443–1446, 1998.

[9] Peleg S. Porat B, “Linear FM signal parameter estimation from discrete–time observations,”IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 4, pp. 607–616, 1991.

[10] Djuric PM. Kay SM, “Parameter estimation of chirp signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 38, No. 12, pp. 2118–2126, 1990.

[11] O’Shea P, “Fast parameter estimation algorithms for linear FM signals,” IEEE International Conference on Acoustics, Speech and Signal Processing, Adelaide, SA, Australia, pp. 17–20, 1994.

[12] Porat B, “Digital processing of random signals: theory and methods,” Prentice Hall Information and System Sciences Series, Englewood Cliffs, NJ, USA: Prentice Hall,1994, ISBN: 9780486462981.

[13] M. G. Christensen, L. J. Højvang, A. Jakobsson, and S. H. Jensen, “Joint fundamental frequency and order estimation using optimal filtering,” EURASIPJ. Adv. Signal Process, Vol. 2011, No. 1, pp. 1–18, June 2011.

[14] P. Stoica and R. L. Moses, “Spectral analysis of signals,” Pearson/Prentice Hall Upper Saddle River, NJ, (2005). ISBN: 0131139568

[15] Kay S, “Signal fitting with uncertain basis functions,” IEEE Signal Processing Letters., Vol. 6, no 18, pp. 383–386, 2011.

[16] Kay SM, “Fundamentals of Statistical Signal Processing: Practical Algorithm. Development,” Vol. 3. Pearson Education, 2013. ISBN: 978–0132808033

[17] Sahay S.B. Meghasyam T. Roy R.K, “Parameter estimation of linear and quadratic chirps by employing the fractional fourier transform and a generalized time frequency transform,”Indian Academy of Sciences, Sadhan Journal, Vol. 40, No. 4, pp. 1049–1075, 2015.

[18] Ikram MZ. Abed–Meraim K. Hua Y, “Estimating the parameters of chirp signals: an iterative approach,” IEEE Transactions on Signal Processing, Vol. 46, No. 12, pp. 3436–3441, 1998.

[19] Xiang-Gen Xia, "Discrete Chirp-Fourier Transform and Its Applicationto Chirp Rate Estimation,” IEEE Trans. Signal Processing, VOL. 48, NO. 11, November 2000.

[20] S. Fallah Tafty, M. Karimi, “Estimating the Frequency of a Complex Exponential and Parameters of Chirp Signal in Noise,” MSc thesis, Dept. Electron. Eng., Shiraz Univ., Shiraz, Iran, 2016.

[21] S. Fallah Tafty, M. Karimi, M. Behzad Fallahpour, “Improvement of the Accuracy and Reduction of the Computational Complexity of the Discrete Polynomial-Phase Transform Method for the Estimation of Chirp Signal Parameters,” Journal of Radar, vol. 5, No. 2, 2017.

[22] S. Fallah Tafty, M. Karimi, “A Combined Method for Estimating the Frequency of a Complex Exponential,” 24th Iranian Conference on Electrical Engineering (ICEE), 2016.

Majlesi Journal of Electrical Engineering

Investigating Bias of DCFT, DPT and Promoted DPT Methods in terms of Phase Parameters Estimation of Chirp Signal

References

References

Volume 15, Issue 3 - Serial Number 3
September 2021
Pages 35-44

Investigating Bias of DCFT, DPT and Promoted DPT Methods in terms of Phase Parameters Estimation of Chirp Signal

References

References

Volume 15, Issue 3 - Serial Number 3September 2021Pages 35-44

Volume 15, Issue 3 - Serial Number 3
September 2021
Pages 35-44