access icon free Instantaneous fundamental frequency estimation of non-stationary periodic signals using non-linear recursive filters

This paper presents an algorithm for estimating the instantaneous fundamental frequency of a noisy non-stationary periodic signal whose components are harmonically related. To this end, the authors’ propose a harmonic state-space model for the input signal and use it to derive an extended Kalman filter (EKF), an unscented Kalman filter (UKF) and a particle filter (PF). In this model, the input signal is characterised by a time-varying fundamental frequency and amplitude which is a practical assumption for real-world periodic signals. In contrast to most of existing methods such as short-time Fourier transform, the proposed algorithm does not use any windowing technique. Therefore the trade-off between time and frequency resolutions is less controversial and so can be used for real-time frequency tracking. It also reveals some fine and continuous variations in signal pitch such as Vibrato and Glissando. Simulation results show that the proposed algorithm performs well even when most of the signal energy is contained in the higher-order harmonics. The performance of the proposed algorithm using EKF, UKF and PF is also evaluated and the results are compared in diverse conditions.

Inspec keywords: signal resolution; recursive filters; particle filtering (numerical methods); state-space methods; Kalman filters; frequency estimation; nonlinear filters

Other keywords: time resolution; higher-order harmonics; frequency resolution; EKF derivation; UKF derivation; unscented Kalman filter; nonlinear recursive filter; nonstationary periodic signal time-varying fundamental frequency estimation; particle filter; frequency tracking; PF derivation; harmonic state-space model; time-varying fundamental amplitude; extended Kalman filter

Subjects: Other topics in statistics; Filtering methods in signal processing; Signal processing theory; Other topics in statistics

References

    1. 1)
    2. 2)
    3. 3)
      • 40. Nielsen, J.K.: ‘Some new results on the estimation of sinusoids in noise’. PhD thesis, Aalborg University, 2012.
    4. 4)
      • 38. Hajimolahoseini, H., Taban, M.R., Abutalebi, H.R.: ‘Improvement of extended Kalman filter frequency tracker for nonstationary harmonic signals’. Int. Symp. on Telecommunications, IEEE, Tehran, August 2008, pp. 592597.
    5. 5)
      • 23. Sun, X.: ‘Pitch determination and voice quality analysis using subharmonic-to-harmonic ratio’. IEEE Int. Conf. on. Acoustics, Speech, and Signal Processing (ICASSP), IEEE, Florida, USA, May 2002, 1, pp. I333.
    6. 6)
    7. 7)
      • 45. Enescu, M., Sirbu, M., Koivunen, V.: ‘Recursive estimation of noise statistics in Kalman filter based MIMO equalization’. Proc. of XXVIIth General Assembly of the Int. Union of Radio Science (URSI), Netherland, 17–24 August 2002.
    8. 8)
    9. 9)
    10. 10)
    11. 11)
      • 24. Drugman, T., Alwan, A.: ‘Joint robust voicing detection and pitch estimation based on residual harmonics’. Proc. Interspeech, Florence, Italy, 2011, pp. 19731976.
    12. 12)
    13. 13)
      • 28. Kawahara, H., Morise, M., Takahashi, T., Nisimura, R., Irino, T., Banno, H.: ‘Tandem-straight: a temporally stable power spectral representation for periodic signals and applications to interference-free spectrum, f0, and aperiodicity estimation’. Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP). IEEE, USA, 2008, pp. 39333936.
    14. 14)
    15. 15)
    16. 16)
    17. 17)
      • 41. Haykin, S.: ‘Communication systems’ (John Wiley and Sons Ltd, New York, 2000, 4th edn.).
    18. 18)
      • 3. Christensen, M.G., Jakobsson, A., Jensen, S.H.: ‘Multi-pitch estimation using harmonic music’. Rec. Asilomar Conf. Signals, Systems, and Computers, November 2006, pp. 521524.
    19. 19)
      • 9. Beigi, H.: ‘Fundamentals of speaker recognition’ (Springer, New York, 2011).
    20. 20)
    21. 21)
    22. 22)
      • 39. Ribeiro, M.I.: ‘Kalman and extended Kalman filters: concept, derivation and properties’ (Institute for Systems and Robotics, Instituto Superior Tcnico, Av. Rovisco Pais, 1, Portugal, 2004).
    23. 23)
    24. 24)
    25. 25)
    26. 26)
      • 6. Hajimolahoseini, H., Taban, M.R., Abutalebi, H.R.: ‘Automatic transcription of music signal using harmonic elimination method’. Int. Symp. on Telecommunications, IEEE, Tehran, August 2008, pp. 559563.
    27. 27)
      • 10. Babacan, O., Drugman, T., Alessandro, N., Henrich, N., Dutoit, T.: ‘A comparative study of pitch extraction algorithms on a large variety of singing sounds’. Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013, pp. 78157819.
    28. 28)
    29. 29)
    30. 30)
      • 8. Jurafsky, D., Martin, J.H.: ‘Speech and language processing’ (Pearson Prentice-Hall, New Jersey, 2008, 2nd edn.).
    31. 31)
    32. 32)
      • 49. Wan, E.A., Merwe, V.: ‘Kalman filtering and neural networks, chapter 7, the unscented Kalman filter’ (Wiley Publishing, New York, 2001).
    33. 33)
      • 48. Gibbs, B.P.: ‘Advanced Kalman filtering, least-squares and modeling: a practical handbook’ (Wiley, New York, 2011).
    34. 34)
    35. 35)
      • 17. Gerhard, D.: ‘Pitch extraction and fundamental frequency: history and current techniques’ (University of Regina, Canada, 2003), pp. 20032006.
    36. 36)
    37. 37)
    38. 38)
      • 33. Christensen, M.G.: ‘A method for low-delay pitch tracking and smoothing’. Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), Japan, March 2012, pp. 345348.
    39. 39)
      • 1. Cemgil, A.T.: ‘Bayesian music transcription’. PhD thesis, Radboud University of Nijmegen, 2004.
    40. 40)
    41. 41)
    42. 42)
    43. 43)
      • 51. Gordon, N., Salmond, D., Smith, A.F.M.: ‘Novel approach to nonlinear and non-Gaussian Bayesian state estimation’, IEE Proc., F, 1993, 140, (2), pp. 107113.
    44. 44)
    45. 45)
      • 44. Mehr, R.K.: ‘On the identification of variances and adaptive Kalman filtering’, IEEE Trans. Autom. Control, 1974, AC-15, (2), pp. 175184.
    46. 46)
      • 4. Hajimolahoseini, H.: ‘Monophonic music transcription’. MS thesis, Yazd University, Iran, 2008.
    47. 47)
      • 30. Kim, S., Paul, A.S., Wan, E.A., McNames, J.: ‘Multiharmonic frequency tracking method using the sigma-point Kalman smoother’, EURASIP J. Adv. Signal Process., 2010, 2010, 36.
    48. 48)
      • 32. Christensen, M.G., Jakobsson, A.: ‘Multi-pitch estimation’ (Morgan & Claypool Publishers, California, 2009).
    49. 49)
    50. 50)
      • 20. Boersma, P.: ‘Accurate short-term analysis of the fundamental frequency and the harmonics-to-noise ratio of a sampled sound’. IFA Proc. Institute of Phonetic Sciences, University of Amsterdam, 1993, pp. 97110.
    51. 51)
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