Construction of positive time-frequency distributions

A general method for constructing nonnegative definite, joint time-frequency distributions (TFDs) satisfying the marginals of time |s(t)|/sup 2/ and frequency |S(f)|/sup 2/ is presented. As nonnegative-definite distributions with the correct marginals, these TFDs are members of the Cohen-Posch class. Several examples illustrating properties of these TFDs are presented for both synthetic and real signals. >

[1]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[2]  Robert L. Burr.  Iterative convex I-projection algorithms for maximum entropy and minimum cross-entropy computations , 1989, IEEE Trans. Inf. Theory.

[3]  Leon Cohen,et al.  Local Bandwidth And Optimal Windows For The Short Time Fourier Transform , 1989, Optics & Photonics.

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

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

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

[7]  Douglas L. Jones,et al.  A simple scheme for adapting time-frequency representations , 1994, IEEE Trans. Signal Process..

[8]  P.J. Loughlin,et al.  Proper time-frequency energy distributions and the Heisenberg uncertainty principle , 1992, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.

[9]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[10]  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..

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

[12]  Les E. Atlas,et al.  Applications of positive time-frequency distributions to speech processing , 1994, IEEE Trans. Speech Audio Process..

[13]  Douglas L. Jones,et al.  A high resolution data-adaptive time-frequency representation , 1990, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[14]  Patrick J. Loughlin,et al.  Deconvolution for positive time-frequency distributions , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[15]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[16]  J. Ville.  THEORY AND APPLICATION OF THE NOTION OF COMPLEX SIGNAL , 1958 .

[17]  B. Hannaford,et al.  Approximating time-frequency density functions via optimal combinations of spectrograms , 1994, IEEE Signal Processing Letters.

[18]  Leon Cohen,et al.  Instantaneous Frequency, Its Standard Deviation And Multicomponent Signals , 1988, Optics & Photonics.

[19]  Leon Cohen,et al.  Positive time-frequency distribution functions , 1985, IEEE Trans. Acoust. Speech Signal Process..

[20]  L. Cohen.  Distributions concentrated along the instantaneous frequency , 1990 .

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

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

[23]  R. Johnson,et al.  Properties of cross-entropy minimization , 1981, IEEE Trans. Inf. Theory.

[24]  Patrick J. Loughlin,et al.  An information-theoretic approach to positive time-frequency distributions , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  Dennis Gabor,et al.  Theory of communication , 1946 .

[26]  J. K. Ord,et al.  Families of frequency distributions , 1973 .

[27]  W. D. Mark.  Spectral analysis of the convolution and filtering of non-stationary stochastic processes , 1970 .

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