A Robust and Computationally Efficient Subspace-Based Fundamental Frequency Estimator

This paper presents a method for high-resolution fundamental frequency (F 0) estimation based on subspaces decomposed from a frequency-selective data model, by effectively splitting the signal into a number of subbands. The resulting estimator is termed frequency-selective harmonic MUSIC (F-HMUSIC). The subband-based approach is expected to ensure computational savings and robustness. Additionally, a method for automatic subband signal activity detection is proposed, which is based on information-theoretic criterion where no subjective judgment is needed. The F-HMUSIC algorithm exhibits good statistical performance when evaluated with synthetic signals for both white and colored noises, while its evaluation on real-life audio signal shows the algorithm to be competitive with other estimators. Finally, F-HMUSIC is found to be computationally more efficient and robust than other subspace-based F 0 estimators, besides being robust against recorded data with inharmonicities.

[1]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[2]  M. Beckman,et al.  Linguistic Models of F0 Use, Physiological Models of F0 Control, and the Issue of “Mean Response Time” , 1999, Language and speech.

[3]  M.G. Christensen,et al.  Multi-Pitch Estimation Using Harmonic Music , 2006, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers.

[4]  Andreas Jakobsson,et al.  Sinusoidal Order Estimation Using Angles between Subspaces , 2009, EURASIP J. Adv. Signal Process..

[5]  Andreas Jakobsson,et al.  Joint High-Resolution Fundamental Frequency and Order Estimation , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[6]  Philip Rose.  On the non-equivalence of fundamental frequency and pitch in tonal description , 1988 .

[7]  M. Bartlett.  A Note on the Multiplying Factors for Various χ2 Approximations , 1954 .

[8]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[9]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[10]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[11]  A. Jakobsson,et al.  Sinusoidal Order Estimation using the Subspace Orthogonality and Shift-Invariance Properties , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[12]  A Lewis,et al.  THE SCIENCE OF SOUND , 1997 .

[13]  Andreas Jakobsson,et al.  Subspace-based fundamental frequency estimation , 2004, 2004 12th European Signal Processing Conference.

[14]  Wolfgang Hess.  Manual and Instrumental Pitch Determination, Voicing Determination , 1983 .

[15]  Petre Stoica,et al.  Frequency-domain method based on the singular value decomposition for frequency-selective NMR spectroscopy. , 2003, Journal of magnetic resonance.

[16]  T. McKelvey,et al.  A robust frequency domain subspace algorithm for multi-component harmonic retrieval , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[17]  S. H. Jensen,et al.  Frequency selective sinusoidal order estimation , 2007 .

[18]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[19]  Valentin Emiya.  Transcription automatique de la musique de piano , 2008 .

[20]  Joseph M. Francos,et al.  Bounds for estimation of complex exponentials in unknown colored noise , 1995, IEEE Trans. Signal Process..

[21]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[22]  Torsten Söderström,et al.  Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies , 1991, IEEE Trans. Signal Process..

[23]  S. Schwerman,et al.  The Physics of Musical Instruments , 1991 .

[24]  Andreas Jakobsson,et al.  Multi-Pitch Estimation , 2009, Multi-Pitch Estimation.

[25]  T. McKelvey,et al.  High SNR performance analysis of F-ESPRIT , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[26]  Andreas Jakobsson,et al.  Cisoid parameter estimation in the colored noise case: asymptotic Cramer-Rao bound, maximum likelihood, and nonlinear least-squares , 1997, IEEE Trans. Signal Process..

[27]  Roland Badeau,et al.  A new perturbation analysis for signal enumeration in rotational invariance techniques , 2006, IEEE Transactions on Signal Processing.

[28]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[29]  Wolfgang J. Hess,et al.  Pitch and voicing determination , 1992 .

[30]  Andreas Jakobsson,et al.  Robust subspace-based fundamental frequency estimation , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[31]  Roland Badeau,et al.  A Parametric Method for Pitch Estimation of Piano Tones , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[32]  Jian Li,et al.  Computationally efficient parameter estimation for harmonic sinusoidal signals , 2000, Signal Process..

[33]  Hideki Kawahara,et al.  YIN, a fundamental frequency estimator for speech and music. , 2002, The Journal of the Acoustical Society of America.