A Tutorial on Non-Parametric Bilinear Time-Frequency Signal Representations

Nonstationary signals have a time-dependent spectral content. This is in contrast to stationary signals whose energy spectrum characterizes their spectral content and that is independent of time. Therefore, nonstationary signals require joint time—frequency representations.

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

[2]  Patrick Flandrin,et al.  An interpretation of the Pseudo-Wigner-Ville distribution , 1984 .

[3]  Franz Hlawatsch Transformation, inversion and conversion of bilinear signal representations , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  B. Atal,et al.  Generalized Short‐Time Power Spectra and Autocorrelation Functions , 1962 .

[5]  P. Flandrin,et al.  Time and frequency representation of finite energy signals: A physical property as a result of an hilbertian condition , 1980 .

[6]  G. Ruggeri On Phase-Space Description of Quantum Mechanics , 1971 .

[7]  Mj Martin Bastiaans A Sampling Theorem For The Complex Spectrogram, And Gabor's Expansion Of A Signal In Gaussian Elementary Signals , 1981 .

[8]  Gloria Faye Boudreaux-Bartels,et al.  Time-frequency signal processing algorithms: analysis and synthesis using wigner distributions , 1984 .

[9]  Thomas W. Parks,et al.  Signal estimation using modified Wigner distributions , 1984, ICASSP.

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

[11]  Ben R. Breed,et al.  A range and azimuth estimator based on forming the spatial Wigner distribution , 1984, ICASSP.

[12]  M. Ackroyd Instantaneous and time-varying spectraߞan introduction , 1970 .

[13]  Irving S. Reed,et al.  A generalization of the Gabor-Helstrom transform (Corresp.) , 1967, IEEE Trans. Inf. Theory.

[14]  A. Royer Wigner function as the expectation value of a parity operator , 1977 .

[15]  Patrick Flandrin,et al.  Representations temps-frequence et causalite , 1985 .

[16]  Boualem Boashash,et al.  Wigner-Ville analysis of time-varying signals , 1982, ICASSP.

[17]  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.

[18]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[19]  R. F. O'Connell,et al.  The Wigner distribution function—50th birthday , 1983 .

[20]  M. Berry Semi-classical mechanics in phase space: A study of Wigner’s function , 1977, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[21]  Mj Martin Bastiaans Sampling theorem for the complex spectrogram, and Gabor's expansion in Gaussian elementary signals , 1981 .

[22]  R. F. Harrison,et al.  Wigner-Ville and evolutionary spectra for covariance equivalent nonstationary random processes , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[24]  K. Kodera,et al.  A new method for the numerical analysis of nonstationary signals , 1976 .

[25]  K. Kodera,et al.  Analysis of time-varying signals with small BT values , 1978 .

[26]  J. G. Krüger,et al.  Quantum mechanics in phase space , 1976 .

[27]  August W. Rihaczek,et al.  Signal energy distribution in time and frequency , 1968, IEEE Trans. Inf. Theory.

[28]  Augustus J. E. M. Janssen,et al.  Gabor representation and Wigner distribution of signals , 1984, ICASSP.

[29]  J. E. Moyal Quantum mechanics as a statistical theory , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[30]  C. Page Instantaneous Power Spectra , 1952 .

[31]  Yves Grenier,et al.  Time-dependent ARMA modeling of nonstationary signals , 1983 .

[32]  M. Ackroyd Short‐Time Spectra and Time‐Frequency Energy Distributions , 1971 .

[33]  R. Altes Detection, estimation, and classification with spectrograms , 1980 .

[34]  M. Bastiaans,et al.  The Wigner distribution function and its applications to optics , 1980 .

[35]  M. Bastiaans,et al.  Gabor's expansion of a signal into Gaussian elementary signals , 1980, Proceedings of the IEEE.

[36]  Mj Martin Bastiaans Transport Equations for the Wigner Distribution Function in an Inhomogeneous and Dispersive Medium , 1979 .

[37]  Walter Schempp,et al.  Radar Ambiguity Functions, Nilpotent Harmonic Analysis, and Holomorphic Theta Series , 1984 .

[38]  Mj Martin Bastiaans The Wigner distribution function and Hamilton's characteristics of a geometric-optical system , 1979 .

[39]  P. Flandrin,et al.  Detection of changes of signal structure by using the Wigner-Ville spectrum , 1985 .

[40]  W. Martin,et al.  Time-frequency analysis of random signals , 1982, ICASSP.

[41]  Jae Lim,et al.  Signal reconstruction from short-time Fourier transform magnitude , 1983 .

[42]  W. Martin Measuring the degree of non-stationarity by using the Wigner-Ville spectrum , 1984, ICASSP.

[43]  R. Fano Short‐Time Autocorrelation Functions and Power Spectra , 1950 .

[44]  O. Grace Instantaneous power spectra , 1981 .

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

[46]  Patrick Flandrin,et al.  Sur les conditions physiques assurant l'unicite de la representation de wigner-ville comme representation temps-frequence , 1983 .

[47]  Harry Wechsler,et al.  The composite pseudo Wigner distribution (CPWD): A computable and versatile approximation to the Wigner distribution (WD) , 1983, ICASSP.

[48]  T. Claasen,et al.  The aliasing problem in discrete-time Wigner distributions , 1983 .

[49]  Guy Melard Propriétés du spectre évolutif d'un processus non stationnaire , 1978 .

[50]  Richard Tolimieri,et al.  Characterizing the radar ambiguity functions , 1984, IEEE Trans. Inf. Theory.

[51]  D. Friedman,et al.  Instantaneous-frequency distribution vs. time: An interpretation of the phase structure of speech , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[52]  A. Lohmann,et al.  The wigner distribution function and its optical production , 1980 .

[53]  A. Janssen Positivity of Weighted Wigner Distributions , 1981 .

[54]  Thomas W. Parks,et al.  Reducing aliasing in the Wigner distribution using implicit spline interpolation , 1983, ICASSP.

[55]  Mj Martin Bastiaans Transport equations for the Wigner distribution function , 1979 .

[56]  M. H. Ackroyd,et al.  Instantaneous spectra and instantaneous frequency , 1970 .

[57]  F. Taylor,et al.  The wigner distribution in speech processing applications , 1984 .

[58]  Leon Cohen,et al.  Distributions in signal theory , 1984, ICASSP.

[59]  A. Janssen Positivity properties of phase-plane distribution functions , 1984 .

[60]  Bernard Escudie,et al.  Représentation hilbertienne et représentation conjointe en temps et fréquence des signaux d'énergie finie, interprétation physique en fonction des observations , 1977 .

[61]  M. Scully,et al.  Distribution functions in physics: Fundamentals , 1984 .

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

[63]  Alwyn van der Merwe,et al.  Perspectives in quantum theory , 1971 .

[64]  Theo A. C. M. Claasen,et al.  On the time-frequency discrimination of energy distributions: Can they look sharper than Heisenberg ? , 1984, ICASSP.

[65]  Bernard Escudie,et al.  Représentation en temps et fréquence des signaux d’énergie finie: analyse et observation des signaux , 1979 .

[66]  de Ng Dick Bruijn,et al.  Uncertainty principles in Fourier analysis , 1967 .

[67]  Jae S. Lim,et al.  Algorithms for signal reconstruction from short-time Fourier transform magnitude , 1983, ICASSP.

[68]  Mj Martin Bastiaans Wigner distribution function and its application to first-order optics , 1979 .

[69]  R. Gendrin,et al.  Unambiguous determination of fine structures in multicomponent time-varying signals , 1979 .

[70]  L. Cohen Positive and Negative Joint Quantum Distributions , 1986 .

[71]  Bernard Escudié,et al.  Principe et mise en œuvre de l'analyse temps fréquence par transformation de Wigner-Ville , 1985 .

[72]  Jae S. Lim,et al.  Signal estimation from modified short-time Fourier transform , 1983, ICASSP.

[73]  J.B. Allen,et al.  A unified approach to short-time Fourier analysis and synthesis , 1977, Proceedings of the IEEE.

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

[75]  N. Marcuvitz Quasiparticle view of wave propagation , 1980, Proceedings of the IEEE.

[76]  Lawrence R. Rabiner,et al.  Short-time Fourier analysis tecniques for FIR system identification and power spectrum estimation , 1979 .

[77]  M. Bastiaans Wigner distribution function display: a supplement to ambiguity function display using a single 1-D input. , 1980, Applied optics.

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

[79]  Harry Wechsler,et al.  A paradigm for invariant object recognition of brightness, optical flow and binocular disparity images , 1982, Pattern Recognit. Lett..

[80]  Harinath Garudadri,et al.  Identification of invariant acoustic cues in stop consonants using the Wigner distribution , 1987 .

[81]  L. Cohen,et al.  Probabilities in Quantum Mechanics , 1967 .

[82]  N. Marinovic,et al.  Use of the Wigner Distribution to Analyze the Time-Frequency Response of Ultrasonic Transducers , 1984 .

[83]  Leon Cohen Properties of the positive time-frequency distribution functions , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[84]  Boualem Boashash,et al.  Recognition of time-varying signals in the time-frequency domain by means of the Wigner distribution , 1984, ICASSP.

[85]  Kai-Bor Yu,et al.  Signal synthesis from Wigner distribution , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[86]  J. Wilbur,et al.  Time and spatial varying CAM and AI signal analysis using the Wigner distribution , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[87]  Carl W. Helstrom,et al.  An expansion of a signal in Gaussian elementary signals (Corresp.) , 1966, IEEE Trans. Inf. Theory.

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

[89]  J. A. Blodgett,et al.  Wigner distribution and ambiguity function , 1980 .

[90]  Theo A. C. M. Claasen,et al.  Time-frequency signal analysis by means of the Wigner distribution , 1981, ICASSP.

[91]  H. Szu Two -dimensional optical processing of one- dimensional acoustic data , 1982 .

[92]  Philip M. Woodward,et al.  Probability and Information Theory with Applications to Radar , 1954 .

[93]  B. V. K. Vijaya Kumar,et al.  Performance Of Wigner Distribution Function Based Detection Methods , 1984 .

[94]  Mj Martin Bastiaans The Wigner distribution function applied to optical signals and systems , 1978 .

[95]  G. Eichmann,et al.  An expansion of Wigner distribution and its applications , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[96]  Alan V. Oppenheim,et al.  Speech spectrograms using the fast Fourier transform , 1970, IEEE Spectrum.

[97]  A. J. E. M. Janssen,et al.  A Note on Hudson’s Theorem about Functions with Nonnegative Wigner Distributions , 1984 .

[98]  Georges Bonnet,et al.  Considérations sur la représentation et l’analyse harmonique des signaux déterministes ou aléatoires , 1968 .

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

[100]  Yves Grenier,et al.  Comparaison des représentations temps-fréquence de signaux présentant des discontinuités spectrales , 1983 .

[101]  B E Saleh,et al.  Generation of the Wigner distribution function of two-dimensional signals by a parallel optical processor. , 1984, Optics letters.

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

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

[104]  E. Wigner On the quantum correction for thermodynamic equilibrium , 1932 .

[105]  David S. K. Chan,et al.  A non-aliased discrete-time Wigner distribution for time-frequency signal analysis , 1982, ICASSP.

[106]  de Ng Dick Bruijn A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence , 1973 .

[107]  Morris J. Levin,et al.  Instantaneous spectra and ambiguity functions (Corresp.) , 1964, IEEE Trans. Inf. Theory.

[108]  P. Flandrin,et al.  A general class of estimators for the wigner-ville spectrum of non-stationary processes , 1984 .

[109]  D. Tj⊘stheim Spectral generating operators for non-stationary processes , 1976, Advances in Applied Probability.