# A Modified Viterbi Algorithm-Based IF Estimation Algorithm for Adaptive Directional Time–Frequency Distributions

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## Abstract

Time–frequency (TF)-based instantaneous frequency estimation algorithms fail to achieve the desired performance when the underlying TF distribution suffers from low resolution of the signal components or signal components intersect each other in the TF domain. This paper addresses above-mentioned problems by (a) employing adaptive directional time–frequency distributions for resolving close components and (b) developing a variant of the Viterbi algorithm that employs both the direction and amplitude of the signal components for IF estimation of crossing components at low signal-to-noise ratio. Experimental results indicate that the proposed method outperforms state-of-the-art methods such as original Viterbi-based IF estimation algorithm and ridge path regrouping methods.

## Keywords

Instantaneous frequency estimation Adaptive time–frequency analysis Intersecting components Adaptive directional time–frequency distribution## References

- 1.S. Ali, N. Khan, M. Haneef, X. Luo, Blind source separation schemes for mono-sensor and multi-sensor systems with application to signal detection. Circuits Syst. Signal Process.
**36**(11), 4615–4636 (2017)MathSciNetCrossRefGoogle Scholar - 2.M.G. Amin, D. Borio, Y. Zhang, L. Galleani, Time–frequency analysis for GNSSs: from interference mitigation to system monitoring. IEEE Signal Process. Mag.
**34**(5), 85–95 (2017)CrossRefGoogle Scholar - 3.F. Auger, P. Flandrin, Y.-T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, H.-T. Wu, Time–frequency reassignment and synchrosqueezing: an overview. IEEE Signal Process. Mag.
**30**(6), 32–41 (2013)CrossRefGoogle Scholar - 4.B. Barkat, K. Abed-Meraim, Algorithms for blind components separation and extraction from the time–frequency distribution of their mixture. EURASIP J. Adv. Signal Process.
**2004**, 978487 (2004)CrossRefGoogle Scholar - 5.B. Boashash, N.A. Khan, T. Ben-Jabeur, Time–frequency features for pattern recognition using high-resolution TFDs: a tutorial review. Digit. Signal Process.
**40**, 1–30 (2015)MathSciNetCrossRefGoogle Scholar - 6.S. Chen, X. Dong, G. Xing, Z. Peng, W. Zhang, G. Meng, Separation of overlapped non-stationary signals by ridge path regrouping and intrinsic chirp component decomposition. IEEE Sens. J.
**17**(18), 5994–6005 (2017)CrossRefGoogle Scholar - 7.C. Conru, I. Djurović, C. Ioana, L. Stanković, Time–frequency detection using Gabor filter bank and Viterbi based grouping algorithm, in
*IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)*(2005)Google Scholar - 8.K. Czarnecki, The instantaneous frequency rate spectrogram. Mech. Syst. Signal Process.
**66**, 361–373 (2016)CrossRefGoogle Scholar - 9.K. Czarnecki, D. Fourer, F. Auger, M. Rojewski, A fast time–frequency multi-window analysis using a tuning directional kernel. Signal Process.
**147**, 110–119 (2018)CrossRefGoogle Scholar - 10.I. Djurović, QML-RANSAC instantaneous frequency estimator for overlapping multicomponent signals in the time–frequency plane. IEEE Signal Process. Lett.
**25**(3), 447–451 (2018)CrossRefGoogle Scholar - 11.I. Djurović, L. Stanković, An algorithm for the Wigner distribution based instantaneous frequency estimation in a high noise environment. Signal Process.
**84**(3), 631–643 (2004)CrossRefGoogle Scholar - 12.I. Djurović, L. Stanković, Modification of the ICI rule-based IF estimator for high noise environments. IEEE Trans. Signal Process.
**52**(9), 2655–2661 (2004)CrossRefGoogle Scholar - 13.X. Dong, S. Chen, G. Xing, Z. Peng, W. Zhang, G. Meng, Doppler frequency estimation by parameterized time–frequency transform and phase compensation technique. IEEE Sens. J.
**18**(9), 3734–3744 (2018)CrossRefGoogle Scholar - 14.M.K. Emresoy, A. El-Jaroudi, Iterative instantaneous frequency estimation and adaptive matched spectrogram. Signal Process.
**64**(2), 157–165 (1998)CrossRefGoogle Scholar - 15.F. Hlawatsch, F. Boudreaux-Bartels, Linear and quadratic time–frequency signal representations. IEEE Signal Process. Mag.
**9**(2), 21–67 (1992)CrossRefGoogle Scholar - 16.N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.-C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, in
*Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences*, vol 454 (The Royal Society, 1998), p. 903–995Google Scholar - 17.V. Katkovnik, L. Stanković, Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length. IEEE Trans. Signal Process.
**46**(9), 2315–2325 (1998)CrossRefGoogle Scholar - 18.N.A. Khan, S. Ali, Sparsity-aware adaptive directional time–frequency distribution for source localization. Circuits Syst. Signal Process.
**37**(3), 1223–1242 (2018)MathSciNetCrossRefGoogle Scholar - 19.N. Khan, B. Boashash, Multi-component instantaneous frequency estimation using locally adaptive directional time frequency distributions. Int. J. Adapt. Control Signal Process.
**30**(3), 429–442 (2016)MathSciNetCrossRefGoogle Scholar - 20.N. Khan, P. Jonsson, M. Sandsten, Performance comparison of time–frequency distributions for estimation of instantaneous frequency of heart rate variability signals. Appl. Sci.
**7**(3), 1–16 (2017)Google Scholar - 21.N.A. Khan, S. Ali, A new feature for the classification of non-stationary signals based on the direction of signal energy in the time–frequency domain. Comput. Biol. Med.
**100**, 10–16 (2018)CrossRefGoogle Scholar - 22.P. Li, Q.-H. Zhang, An improved Viterbi algorithm for IF extraction of multicomponent signals. Signal Image Video Process.
**12**(1), 171–179 (2017)CrossRefGoogle Scholar - 23.F. Lurz, S. Lindner, S. Linz, S. Mann, R. Weigel, A. Koelpin, High-speed resonant surface acoustic wave instrumentation based on instantaneous frequency measurement. IEEE Trans. Instrum. Meas.
**66**(5), 974–984 (2017)CrossRefGoogle Scholar - 24.D. Mikluc, D. Bujaković, M. Andrić, S. Simić, Estimation and extraction of radar signal features using modified B distribution and particle filters. J. RF Eng. Telecommun.
**70**(9–10), 417–427 (2016)Google Scholar - 25.M. Mohammadi, N. Khan, A.A. Pouyan, Automatic seizure detection using a highly adaptive directional time-frequency distribution. Multidimens. Syst. Signal Process.
**29**(4), 1661–1678 (2018)CrossRefGoogle Scholar - 26.M. Mohammadi, A. Pouyan, N. Khan, A highly adaptive directional time–frequency distribution. Signal Image Video Process.
**10**(7), 1369–1376 (2016)CrossRefGoogle Scholar - 27.M. Mohammadi, A.A. Pouyan, N. Khan, V. Abolghasemi, Locally optimized adaptive directional time-frequency distributions. Circuits Syst. Signal Process.
**37**(8), 3154–3174 (2018)MathSciNetCrossRefGoogle Scholar - 28.T.B. Patel, H.A. Patil, Cochlear filter and instantaneous frequency based features for spoofed speech detection. IEEE J. Sel. Top. Signal Process.
**11**(4), 618–631 (2017)CrossRefGoogle Scholar - 29.L. Rankine, M. Mesbah, B. Boashash, IF estimation for multicomponent signals using image processing techniques in the time–frequency domain. Signal Process.
**87**(6), 1234–1250 (2007)CrossRefGoogle Scholar - 30.S. Sandoval, P.L. De Leon, Advances in empirical mode decomposition for computing instantaneous amplitudes and instantaneous frequencies, in
*2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*(2017), p. 4311–4315Google Scholar - 31.L. Stanković, M. Daković, T. Thayaparan,
*Time–Frequency Signal Analysis with Applications*(Artech House, Boston, 2013)zbMATHGoogle Scholar - 32.L. Stanković, I. Djurović, S. Stanković, M. Simeunović, S. Djukanović, M. Daković, Instantaneous frequency in time–frequency analysis: enhanced concepts and performance of estimation algorithms. Digit. Signal Process.
**2**, 1–13 (2014)CrossRefGoogle Scholar - 33.C. Wang, F. Kong, Q. He, F. Hu, F. Liu, Doppler effect removal based on instantaneous frequency estimation and time domain re-sampling for wayside acoustic defective bearing detector system. Measurement
**50**, 346–355 (2014)CrossRefGoogle Scholar - 34.Y. Yang, X. Dong, Z. Peng, W. Zhang, G. Meng, Component extraction for non-stationary multi-component signal using parameterized de-chirping and band-pass filter. IEEE Signal Process. Lett.
**22**(9), 1373–1377 (2015)CrossRefGoogle Scholar