A new method for non-stationary signal analysis using eigenvalue decomposition of the Hankel matrix and Hilbert transform

Non-stationary signal analysis is an essential part for many engineering fields. Time-frequency analysis methods are commonly used methods for analysis of non-stationary signals. In this paper, a new domain for time-frequency analysis has been proposed which has been studied for the analysis of non-stationary signals. The proposed method combines two techniques namely, iterative eigenvalue decomposition of the Hankel matrix (IEVD-HM) and the Hilbert transform (HT). The IEVD-HM technique provides a set of mono-component signals where the HT has been employed to determine amplitude envelopes and instantaneous frequencies of these mono-component signals. These amplitude envelope and instantaneous frequency estimations have been used to determine the time-frequency representation. The obtained time-frequency representation has been studied for the analysis of synthetic non-stationary signals in order to show the effectiveness of the proposed method.

[1]  Norden E. Huang,et al.  A review on Hilbert‐Huang transform: Method and its applications to geophysical studies , 2008 .

[2]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[4]  Ram Bilas Pachori,et al.  Cross-terms reduction in the Wigner-Ville distribution using tunable-Q wavelet transform , 2016, Signal Process..

[5]  Robert B. Dunn,et al.  Adaptive short-time analysis-synthesis for speech enhancement , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[6]  M. Portnoff.  Time-frequency representation of digital signals and systems based on short-time Fourier analysis , 1980 .

[7]  Boualem Boashash,et al.  Time-Frequency Signal Analysis and Processing: A Comprehensive Reference , 2015 .

[8]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..

[9]  T. Claasen,et al.  THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS , 1980 .

[10]  Pooja Jain,et al.  Event-Based Method for Instantaneous Fundamental Frequency Estimation from Voiced Speech Based on Eigenvalue Decomposition of the Hankel Matrix , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[11]  S. Hahn.  Hilbert Transforms in Signal Processing , 1996 .

[12]  Sylvain Meignen,et al.  Time-Frequency Reassignment and Synchrosqueezing: An Overview , 2013, IEEE Signal Processing Magazine.

[13]  Jechang Jeong,et al.  Kernel design for reduced interference distributions , 1992, IEEE Trans. Signal Process..

[14]  Pradip Sircar,et al.  A new technique to reduce cross terms in the Wigner distribution , 2007, Digit. Signal Process..

[15]  Pooja Jain,et al.  An iterative approach for decomposition of multi-component non-stationary signals based on eigenvalue decomposition of the Hankel matrix , 2015, J. Frankl. Inst..

[16]  Valery Naranjo,et al.  Removing interference components in time-frequency representations using morphological operators , 2011, J. Vis. Commun. Image Represent..

[17]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[18]  Y Sheng,et al.  Wavelet transform as a bank of the matched filters. , 1992, Applied optics.

[19]  Shubha Kadambe,et al.  A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform , 1992, IEEE Trans. Signal Process..

[20]  Igor Djurovic,et al.  Robust time-frequency representation based on the signal normalization and concentration measures , 2014, Signal Process..

[21]  Wen-Liang Hwang,et al.  EMD Revisited: A New Understanding of the Envelope and Resolving the Mode-Mixing Problem in AM-FM Signals , 2012, IEEE Transactions on Signal Processing.