STFT With Adaptive Window Width Based on the Chirp Rate

An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To enhance the performance, this method is substantially modified in this paper: i) because the wavelet transform used for instantaneous frequency (IF) estimation is not signal-dependent, a low-complexity ASTFT based on a novel concentration measure is addressed; ii) in order to increase robustness to IF estimation error, the principal component analysis (PCA) replaces the difference operator for calculating the chirp rate; and iii) a more robust Gaussian kernel with time-frequency-varying window width is proposed. Simulation results show that our method has higher energy concentration than the other ASTFTs, especially for multicomponent signals and nonlinear FM signals. Also, for IF estimation, our method is superior to many other adaptive TFRs in low signal-to-noise ratio (SNR) environments.

[1]  Jin Jiang,et al.  Frequency-based window width optimization for S-transform , 2008 .

[2]  Mostefa Mesbah,et al.  IF estimation for multicomponent signals using image processing techniques in the time-frequency domain , 2007, Signal Process..

[3]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[4]  Douglas L. Jones,et al.  A high resolution data-adaptive time-frequency representation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[6]  Jun Xiao,et al.  Multitaper Time-Frequency Reassignment for Nonstationary Spectrum Estimation and Chirp Enhancement , 2007, IEEE Transactions on Signal Processing.

[7]  Soo-Chang Pei,et al.  Energy concentration enhancement using window width optimization in S transform , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Leon Cohen,et al.  Time Frequency Analysis: Theory and Applications , 1994 .

[9]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[10]  Sridhar Krishnan,et al.  Adaptive time-frequency signal analysis and its case study in biomedical ecgwaveform analysis , 2009, 2009 16th International Conference on Digital Signal Processing.

[11]  Guo Jiantao,et al.  Optimal kernel design and time-frequency analysis for frequency hopping signal using entropy measure , 2008, 2008 International Conference on Information and Automation.

[12]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[13]  Jin Jiang,et al.  Time-frequency feature representation using energy concentration: An overview of recent advances , 2009, Digit. Signal Process..

[14]  Cristel Chandre,et al.  Time–frequency analysis of chaotic systems , 2002, nlin/0209015.

[15]  LJubisa Stankovic,et al.  Time-frequency representation based on the reassigned S-method , 1999, Signal Process..

[16]  P. O'Shea.  A new technique for instantaneous frequency rate estimation , 2002, IEEE Signal Processing Letters.

[17]  LJubisa Stankovic,et al.  A measure of some time-frequency distributions concentration , 2001, Signal Process..

[18]  C. Robert Pinnegar,et al.  The S-transform with windows of arbitrary and varying shape , 2003 .

[19]  Jo Lynn Tan,et al.  Adaptive optimal kernel smooth-windowed Wigner-Ville bispectrum for digital communication signals , 2011, Signal Process..

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

[21]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

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

[23]  Bruno Torrésani,et al.  Characterization of signals by the ridges of their wavelet transforms , 1997, IEEE Trans. Signal Process..

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

[25]  Anna Scaglione,et al.  Product high-order ambiguity function for multicomponent polynomial-phase signal modeling , 1998, IEEE Trans. Signal Process..

[26]  Xiang-Gen Xia,et al.  Discrete chirp-Fourier transform and its application to chirp rate estimation , 2000, IEEE Trans. Signal Process..

[27]  Saeed Mian Qaisar,et al.  An Adaptive Resolution Computationally Efficient Short-Time Fourier Transform , 2008, J. Electr. Comput. Eng..

[28]  Lin Wang,et al.  An adaptive Generalized S-transform for instantaneous frequency estimation , 2011, Signal Process..

[29]  P. McFadden,et al.  DECOMPOSITION OF GEAR VIBRATION SIGNALS BY THE GENERALISED S TRANSFORM , 1999 .

[30]  Yigang He,et al.  Frequency estimation of electric signals based on the adaptive short-time Fourier transform , 2009 .

[31]  G Rajshekhar,et al.  Adaptive window Wigner-Ville-distribution-based method to estimate phase derivative from optical fringes. , 2009, Optics letters.

[32]  J. A. López del Val,et al.  Principal Components Analysis , 2018, Applied Univariate, Bivariate, and Multivariate Statistics Using Python.

[33]  M. Behzad,et al.  Time-Frequency Feature Extraction of a Cracked Shaft Using an Adaptive Kernel , 2006 .

[34]  Ljubisa Stankovic,et al.  A multitime definition of the Wigner higher order distribution: L-Wigner distribution , 1994, IEEE Signal Processing Letters.

[35]  C. Robert Pinnegar,et al.  Time-frequency localization with the Hartley S-transform , 2004, Signal Process..

[36]  Richard Kronland-Martinet,et al.  Asymptotic wavelet and Gabor analysis: Extraction of instantaneous frequencies , 1992, IEEE Trans. Inf. Theory.

[37]  Yu Huang,et al.  Time-Frequency Representation Based on an Adaptive Short-Time Fourier Transform , 2010, IEEE Transactions on Signal Processing.

[38]  Bruno Torrésani,et al.  Time-Frequency Jigsaw Puzzle: Adaptive Multiwindow and Multilayered Gabor Expansions , 2007, Int. J. Wavelets Multiresolution Inf. Process..

[39]  Jin Jiang,et al.  A Window Width Optimized S-Transform , 2008, EURASIP J. Adv. Signal Process..

[40]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.