Fast and accurate phase unwrapping

More and more speech technology and signal processing applications make use of the phase information. A proper estimation and representation of the phase goes inextricably along with a correct phase unwrapping, which refers to the problem of finding the instance of the phase function chosen to ensure continuity. This paper proposes a new technique of phase unwrapping which is based on two mathematical considerations: i) a property of the unwrapped phase at Nyquist frequency, ii) the modified Schur-Cohn’s algorithm which allows a fast calculation of the root distribution of polynomials with respect to the unit circle. The proposed method is compared to five state-of-the-art phase unwrappers on a large dataset of both synthetic random and real speech signals. By leveraging the two aforementioned considerations, the proposed approach is shown to perform an exact estimation of the unwrapped phase at a reduced computational load.

[1]  José Tribolet,et al.  A new phase unwrapping algorithm , 1977 .

[2]  Bir Bhanu,et al.  Computation of complex cepstrum. , 1980 .

[3]  A. Oppenheim,et al.  Iterative techniques for minimum phase signal reconstruction from phase or magnitude , 1980 .

[4]  Kenneth Steiglitz,et al.  Phase unwrapping by factorization , 1982 .

[5]  R. Kuc,et al.  A direct relation between a signal time series and its unwrapped phase , 1982 .

[6]  D. S. Mitrinovic,et al.  The Cauchy Method of Residues: Theory and Applications , 1984 .

[7]  J. Scott.  Improving confidence in the phase unwrapping algorithm , 1984 .

[8]  Y. Bistritz.  Zero location with respect to the unit circle of discrete-time linear system polynomials , 1984 .

[9]  Hamid Al-Nashi.  Phase unwrapping of digital signals , 1989, IEEE Trans. Acoust. Speech Signal Process..

[10]  A. Edelman,et al.  Polynomial roots from companion matrix eigenvalues , 1995 .

[11]  Messaoud Benidir.  On the root distribution of general polynomials with respect to the unit circle , 1996, Signal Process..

[12]  I. Ibragimov,et al.  On roots of random polynomials , 1997 .

[13]  Satoshi Nakamura,et al.  Efficient representation of short-time phase based on group delay , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[14]  Peter Bormann,et al.  New Manual of Seismological Observatory Practice , 2002 .

[15]  S. Bhattacharyya,et al.  Root counting, phase unwrapping, stability and stabilization of discrete time systems , 2002 .

[16]  Fabrice Labeau,et al.  Discrete Time Signal Processing , 2004 .

[17]  Rajesh M. Hegde,et al.  Continuous speech recognition using joint features derived from the modified group delay function and MFCC , 2004, INTERSPEECH.

[18]  A. Oppenheim,et al.  Computation of the One-Dimensional Unwrapped Phase , 2007, 2007 15th International Conference on Digital Signal Processing.

[19]  Kuldip K. Paliwal,et al.  Short-time phase spectrum in speech processing: A review and some experimental results , 2007, Digit. Signal Process..

[20]  Thierry Dutoit,et al.  Chirp group delay analysis of speech signals , 2007, Speech Commun..

[21]  Ibon Saratxaga,et al.  Use of harmonic phase information for polarity detection in speech signals , 2009, INTERSPEECH.

[22]  T. Dutoit,et al.  On the mutual information between source and filter contributions for voice pathology detection , 2020, INTERSPEECH.

[23]  Longbiao Wang,et al.  Speaker identification by combining MFCC and phase information in noisy environments , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[24]  Thierry Dutoit,et al.  On the potential of glottal signatures for speaker recognition , 2010, INTERSPEECH.

[25]  Jon Sánchez,et al.  Use of the Harmonic Phase in Speaker Recognition , 2011, INTERSPEECH.

[26]  Thierry Dutoit,et al.  Phase-based information for voice pathology detection , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[27]  Thierry Dutoit,et al.  Causal-anticausal decomposition of speech using complex cepstrum for glottal source estimation , 2011, Speech Commun..

[28]  Axel Röbel,et al.  Function of Phase-Distortion for glottal model estimation , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[29]  Thierry Dutoit,et al.  The Deterministic Plus Stochastic Model of the Residual Signal and Its Applications , 2012, IEEE Transactions on Audio, Speech, and Language Processing.

[30]  Patrick A. Naylor,et al.  Detection of Glottal Closure Instants From Speech Signals: A Quantitative Review , 2012, IEEE Transactions on Audio, Speech, and Language Processing.

[31]  Thomas Drugman,et al.  A new phase-based feature representation for robust speech recognition , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[32]  Benedict Shien Wei Ng,et al.  EEG phase patterns reflect the selectivity of neural firing. , 2013, Cerebral cortex.

[33]  P. Bormann,et al.  Seismic Signals and Noise , 2013 .

[34]  Yannis Stylianou,et al.  The importance of phase on voice quality assessment , 2014, INTERSPEECH.

[35]  Daniel Erro,et al.  A measure of phase randomness for the harmonic model in speech synthesis , 2014, INTERSPEECH.

[36]  Yannis Stylianou,et al.  Maximum Voiced Frequency Estimation: Exploiting Amplitude and Phase Spectra , 2014, IEEE Signal Processing Letters.

[37]  Petra Kaufmann,et al.  Two Dimensional Phase Unwrapping Theory Algorithms And Software , 2016 .