Kernel decomposition of time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved time-frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In the paper, the authors introduce some new tools for the interpretation and quantitative comparison of high-resolution TFDs. These tools are used in related work to define low-cost high-resolution TFDs and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFDs. First, each real-valued TFD is associated with a self-adjoint linear operator /spl psi/. The spectral representation of /spl psi/ expresses the TFD as a weighted sum of spectrograms (SPs). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFDs due to the fact that /spl psi/ is not positive. >

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

[2]  Jechang Jeong,et al.  Alias-free generalized discrete-time time-frequency distributions , 1992, IEEE Trans. Signal Process..

[3]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[4]  William J. Williams,et al.  Decomposition of time-frequency distribution kernels , 1992, Optics & Photonics.

[5]  D. Thomson,et al.  Spectrum estimation and harmonic analysis , 1982, Proceedings of the IEEE.

[6]  W. J. Williams,et al.  Analysis of event related potentials: time-frequency energy distribution. , 1987, Biomedical sciences instrumentation.

[7]  William J. Williams,et al.  Fast implementation of time-frequency distributions , 1992, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.

[8]  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..

[9]  M.G. Amin.  Spectral decomposition of time-frequency distribution kernels , 1994, IEEE Trans. Signal Process..

[10]  Franz Hlawatsch,et al.  Regularity and unitarity of bilinear time-frequency signal representations , 1992, IEEE Trans. Inf. Theory.

[11]  W. Kozek,et al.  Time-frequency subspaces and their application to time-varying filtering , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[12]  William J. Williams,et al.  Fast implementations of generalized discrete time-frequency distributions , 1994, IEEE Trans. Signal Process..

[13]  Langford B. White,et al.  Transition kernels for bilinear time-frequency distributions , 1991, IEEE Trans. Signal Process..

[14]  W. J. Williams,et al.  New time-frequency distributions: theory and applications , 1989, IEEE International Symposium on Circuits and Systems,.

[15]  Douglas L. Jones,et al.  A resolution comparison of several time-frequency representations , 1992, IEEE Trans. Signal Process..

[16]  Ingrid Daubechies,et al.  Time-frequency localization operators: A geometric phase space approach , 1988, IEEE Trans. Inf. Theory.

[17]  William J. Williams,et al.  High-resolution signal synthesis for time-frequency distributions , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[18]  Arch W. Naylor,et al.  Linear Operator Theory in Engineering and Science , 1971 .

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

[20]  Patrick Flandrin,et al.  Some features of time-frequency representations of multicomponent signals , 1984, ICASSP.

[21]  Douglas L. Jones,et al.  Time-frequency window leakage in the short-time Fourier transform , 1987 .

[22]  W. J. Williams,et al.  Mechanism of the cross-terms in spectrograms , 1992, IEEE Trans. Signal Process..

[23]  Cornelis P. Janse,et al.  Time-Frequency Distributions of Loudspeakers: The Application of the Wigner Distribution , 1983 .

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

[25]  Leon Cohen,et al.  Positive quantum joint distributions , 1980 .

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

[27]  D. Barry,et al.  Muscle sounds are emitted at the resonant frequencies of skeletal muscle , 1990, IEEE Transactions on Biomedical Engineering.

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

[29]  Jechang Jeong,et al.  New Time-Frequency Distributions For The Analysis Of Multicomponent Signals , 1989, Optics & Photonics.

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

[31]  Steven M. Sussman,et al.  Least-square synthesis of radar ambiguity functions , 1962, IRE Trans. Inf. Theory.

[32]  Gregory Scott Cunningham.  Analysis, synthesis and implementation of time-frequency distributions using the spectrogram decomposition. , 1992 .

[33]  Leon Cohen,et al.  Generalized ambiguity functions , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[35]  Jae Lim,et al.  Signal estimation from modified short-time Fourier transform , 1984 .

[36]  Thomas W. Parks,et al.  Time-varying filtering and signal estimation using Wigner distribution synthesis techniques , 1986, IEEE Trans. Acoust. Speech Signal Process..

[37]  Fred J. Taylor,et al.  On the Wigner distribution , 1983, ICASSP.