Virtues and vices of quartic time-frequency distributions

We present results concerning three different types of quartic (fourth order) time-frequency distributions (TFDs). First, we present new results on the previously introduced local ambiguity function and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. Second, we introduce the class of quartic, shift-covariant, time-frequency distributions and investigate distributions that localize quadratic chirps. Finally, we present a shift covariant distribution of time and chirp rate.

[1]  Ajem Guido Janssen,et al.  On the locus and spread of pseudo-density functions in the time-frequency plane , 1982 .

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

[3]  Patrick J. Loughlin,et al.  Instantaneous frequency and the conditional mean frequency of a signal , 1997, Signal Process..

[4]  P. Gonçalves,et al.  Geometry of affine time-frequency distributions , 1996 .

[5]  Les E. Atlas,et al.  Bilinear time-frequency representations: new insights and properties , 1993, IEEE Trans. Signal Process..

[6]  H.H. Szu,et al.  The mutual time—Frequency content of two signals , 1984, Proceedings of the IEEE.

[7]  Richard G. Baraniuk.  Covariant time-frequency representations through unitary equivalence , 1996, IEEE Signal Processing Letters.

[8]  Theo A. C. M. Claasen,et al.  On positivity of time-frequency distributions , 1985, IEEE Trans. Acoust. Speech Signal Process..

[9]  Boualem Boashash,et al.  Polynomial time-frequency distributions and time-varying higher order spectra: Application to the analysis of multicomponent FM signals and to the treatment of multiplicative noise , 1998, Signal Process..

[10]  L. Cohen.  Generalized Phase-Space Distribution Functions , 1966 .

[11]  Les E. Atlas,et al.  Construction of positive time-frequency distributions , 1994, IEEE Trans. Signal Process..

[12]  P. Bertrand,et al.  A class of affine Wigner functions with extended covariance properties , 1992 .

[13]  Patrick Flandrin,et al.  Time-Frequency/Time-Scale Analysis , 1998 .

[14]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[15]  John C. Wood,et al.  Radon transformation of time-frequency distributions for analysis of multicomponent signals , 1994, IEEE Trans. Signal Process..

[16]  Ljubisa Stankovic,et al.  On the realization of the polynomial Wigner-Ville distribution for multicomponent signals , 1998, IEEE Signal Processing Letters.

[17]  Douglas L. Jones,et al.  Signal-dependent time-frequency analysis using a radially Gaussian kernel , 1993, Signal Process..

[18]  Charles A. Stutt,et al.  Some results on real-part/imaginary-part and magnitude-phase relations in ambiguity functions , 1964, IEEE Trans. Inf. Theory.

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

[21]  Ljubisa Stankovic,et al.  A method for improved distribution concentration in the time-frequency analysis of multicomponent signals using the L-Wigner distribution , 1995, IEEE Trans. Signal Process..

[22]  Sergio Barbarossa,et al.  Analysis of multicomponent LFM signals by a combined Wigner-Hough transform , 1995, IEEE Trans. Signal Process..

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

[24]  Antonia Papandreou-Suppappola,et al.  The hyperbolic class of quadratic time-frequency representations. I. Constant-Q warping, the hyperbolic paradigm, properties, and members , 1993, IEEE Trans. Signal Process..

[25]  John C. Wood,et al.  Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals , 1994, IEEE Trans. Signal Process..

[26]  Jean-Louis Lacoume,et al.  Construction of fourth-order Cohen's class: A deductive approach , 1992, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.

[27]  W. J. Williams,et al.  A function of time, frequency, lag, and Doppler , 1999, IEEE Trans. Signal Process..

[28]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

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

[30]  Bruno Torrésani,et al.  Time-Frequency and Time-Scale Analysis , 1999 .

[31]  Boualem Boashash,et al.  Kernel design for time-frequency signal analysis using the Radon transform , 1993, IEEE Trans. Signal Process..

[32]  Thomas W. Parks,et al.  The Weyl correspondence and time-frequency analysis , 1994, IEEE Trans. Signal Process..

[33]  S. Kay,et al.  On the optimality of the Wigner distribution for detection , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[34]  Boualem Boashash,et al.  Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra , 1994, IEEE Trans. Signal Process..

[35]  Andrew K. Chan,et al.  Linear frequency-modulated signal detection using Radon-ambiguity transform , 1998, IEEE Trans. Signal Process..

[36]  Chrysostomos L. Nikias,et al.  Wigner Higher Order Moment Spectra: Definition, Properties, Computation and Application to Transient Signal Analysis , 1993, IEEE Trans. Signal Process..

[37]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[38]  François Auger.  Représentations temps-fréquence des signaux non-stationnaires : synthèse et contribution , 1991 .

[39]  John C. Wood,et al.  Radon transformation of time-frequency distributions for analysis of multicomponent signals , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[40]  P. Flandrin,et al.  Two excursions into the quartic domain , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

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

[42]  P. Flandrin,et al.  Chirp hunting , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[43]  William J. Williams,et al.  Quadralinear time-frequency representations , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.