Analysis of multi-component non-stationary signals using Fourier-Bessel transform and Wigner distribution

We present a new method for time-frequency representation (TFR), which combines the Fourier-Bessel (FB) transform and the Wigner-Ville distribution (WVD). The FB transform decomposes a multi-component signal into a number of mono-component signals, and then the WVD technique is applied on each component of the composite signal to analyze its time-frequency distribution (TFD). The simulation results show that the proposed technique based on the FB decomposition is a powerful tool for analyzing multi-component non-stationary signals and for obtaining the TFR of the signal without cross terms.

[1]  Alexander D. Poularikas,et al.  The handbook of formulas and tables for signal processing , 1998 .

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

[3]  Shie Qian,et al.  Decomposition of the Wigner-Ville distribution and time-frequency distribution series , 1994, IEEE Trans. Signal Process..

[4]  Göran Salomonsson,et al.  The use of a filter bank and the Wigner-Ville distribution for time-frequency representation , 1999, IEEE Trans. Signal Process..

[5]  P. Sircar,et al.  A novel technique to reduce cross terms in the squared magnitude of the wavelet transform and the short-time Fourier transform , 2005, IEEE International Workshop on Intelligent Signal Processing, 2005..

[6]  Douglas L. Jones,et al.  A signal-dependent time-frequency representation: optimal kernel design , 1993, IEEE Trans. Signal Process..

[7]  Pradip Sircar,et al.  Complex FM signal model for non-stationary signals , 1997, Signal Process..

[8]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[9]  Alfred Mertins,et al.  Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications , 1999 .

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

[11]  Robert J. Marks,et al.  The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[12]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[13]  Israel Cohen,et al.  Adaptive suppression of Wigner interference-terms using shift-invariant wavelet packet decompositions , 1999, Signal Process..

[14]  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..

[15]  J. Schroeder.  Signal Processing via Fourier-Bessel Series Expansion , 1993 .

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

[17]  Pradip Sircar,et al.  Complex AM signal model for non-stationary signals , 1996, Signal Process..

[18]  Kaliappan Gopalan,et al.  A comparison of speaker identification results using features based on cepstrum and Fourier-Bessel expansion , 1999, IEEE Trans. Speech Audio Process..

[19]  Fikret Gürgen,et al.  Speech enhancement by Fourier-Bessel coefficients of speech and noise , 1990 .