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Introduction to Time-Frequency Signal Analysis

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Wavelet Transforms and Time-Frequency Signal Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Time-frequency signal analysis (TFSA) has developed as a significant field in the area of signal processing. It involves the representation and processing of signals with time-varying spectral characteristics. This chapter presents fundamental principles of TFSA and reviews the main contributions to the field, including the most recent advances, such as polynomial Wigner—Ville distributions (PWVD), the high time-frequency resolution B-distribution, and the instantaneous frequency tracking and estimation.

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References

  1. B. Boashash. Time-frequency signal analysis, inAdvances in Spectrum Analysis and Array Processing(S. Haykin, ed.), Vol. 1, Chap. 9, pp. 418–517, Prentice-Hall, Englewood Cliffs, NJ, 1991.

    Google Scholar 

  2. B. Boashash, ed.Time Frequency Signal AnalysisLongman Chesire, Melbourne, 1992.

    Google Scholar 

  3. B. Boashash. Interpreting and estimating the instantaneous frequency of a signal. Part I: Fundamentals.Proceedings of the IEEEpp. 520–538, April, 1992.

    Google Scholar 

  4. B. Boashash. Interpreting and estimating the instantaneous frequency of a signal. Part II: Algorithms Proceedings of the IEEE, 539–569, April, 1992.

    Google Scholar 

  5. B. Boashash and B. Ristic. A time-frequency perspective of higher-order spectra as a tool for non-stationary signal analysis, InHigher-Order Statistical Signal Processing(B. Boashash and E. J. Powers and A. M. Zoubir, eds.), Chap. 4, Longman Chesire, London, 1995.

    Google Scholar 

  6. B. Boashash, Time-frequency signal analysis, past, present and future trends, inControl and Dynamic Systems(C. T. Leonides, ed.), Vol.78—Digital Control and Signal Processing Systems and TechniquesChap. 1, pp. 1–71, Academic Press, New York, 1996.

    Google Scholar 

  7. B. Boashash. An introduction to time-frequency signal analysis, inProceedings of the Sixth IEEE Inter. Workshop on Intell. Sig. Proc. and Com. SystemsMelbourne, 4–6 Nov. 1998 (Tutorial)

    Google Scholar 

  8. D. Gabor. Theory of CommunicationJ. of IEE 93(1946), 429–457.

    Google Scholar 

  9. J. Ville. Theorie et application de la notion de signal analytiqueCables et Transmissions 2A (1)(1948) 61–74.

    Google Scholar 

  10. C. H. Page. Instantaneous power spectraJ. of Appl. Phys. 23(1)(1953), 103–106.

    Article  Google Scholar 

  11. C. Turner. On the concept of an instantaneous power spectra and its relation to the autocorrelation functionJ. of Appl. Phys. 25(1954), 1347–1351.

    Article  MATH  Google Scholar 

  12. M. Levin. Instantaneous spectra and ambigutiy functionIEEE Trans. Inform. Theory 13(1967), 95–97.

    Article  Google Scholar 

  13. A. Rihaczek. Signal energy distribution in time and frequencyIEEE Trans. Inform. Theory 14(3)(1968), 369–374.

    Article  Google Scholar 

  14. B. Boashash, B. Escudie and J. Komatitsch. Sur la possibilitü d’utiliser la representation conjointe en temps et früquence dans l’ analyse des signaux modulüs en früquence emis en vibrosismiques, in7th Symposium on Signal Processing and its Applicationspp. 121–126, 1979.

    Google Scholar 

  15. T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution—Part 1Phillips J. Res. 35(1980), 217–250.

    Google Scholar 

  16. T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution— Part 2Phillips J. Res. 35(1980), 276–300.

    Google Scholar 

  17. T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution—Part 3Phillips J. Res. 35(1980), 372–389.

    Google Scholar 

  18. B. Boashash, P. Flandrin, B. Escudie, and J. Grea.Positivity of time-frequency distributions C. R. Acad. Sci. Paris(1979).

    Google Scholar 

  19. B. Boashash. Wigner analysis of time-varyirig signals—Its application in seismic prospecting, inProc. EUSIPCOpp. 703–706, 1983.

    Google Scholar 

  20. B. Boashash. Representation conjointe en temps et en frequence des signaux d’energie finie, Technical Report 373 78, Elf-Acquitaine Research Publication, 1978.

    Google Scholar 

  21. J. Jeong and W. J. Williams, Kernel design for reduced interference distributionsIEEE Trans. Signal Process. 40(2)(1992), 402–412.

    Article  Google Scholar 

  22. B. Ristic. Signal dependent and higher-order time-frequency analysis, PhD thesis, Signal Processing Research Centre, Queensland University of Technology, Australia, 1995.

    Google Scholar 

  23. B. Boashash and P. J. O’Shea. Polynomial Wigner–CVille distributions and their relationship to time-varying higher-order spectraIEEE Trans. Signal Process. 42 (1994)216–220.

    Article  Google Scholar 

  24. G. Jones. Time-frequency analysis and the analysis of multicomponent signals, PhD thesis, Queensland University of Technology, 1992.

    Google Scholar 

  25. J. Kay and R. Lerner.Lectures in Communications TheoryMcGraw-Hill, New York, 1961.

    Google Scholar 

  26. C. Helstrom. An expansion of a signal into Gaussian elementary signalsIEEE Trans. Inform. Theory 13(1966), 344–345.

    Google Scholar 

  27. I. Daubeshies. The wavelet transform: A method for time-frequency localisation, inAdvances in Spectral Estimation and Array Processing( S. Haykin, ed.), Prentice Hall, Englewood Cliffs, NJ, 1990.

    Google Scholar 

  28. L. Cohen. Time-frequency distributions—A reviewProc. IEEE 77(1989), 941–981.

    Article  Google Scholar 

  29. B. Boashash. Note on the use of the Wigner distributionIEEE Trans. Acoustics, Speech Signal Process. 36(9)(1988), 1518–1521.

    Article  MATH  Google Scholar 

  30. E. P. Wigner. On the quantum correction for thermodynamic equilibriumPhys. Rev. 40(1932), 748–759.

    Article  Google Scholar 

  31. B. Boashash. Representation temps-frequence. PhD thesis, Dipl. de Docteur-Ingenieur these, University of Grenoble, 1982.

    Google Scholar 

  32. B. Boashash. Note d’information sur la representation des signaux dans le domaine temps-frequence, Technical Report, 135 81, Elf-Aquitaine Research Publication, 1981.

    Google Scholar 

  33. W. Martin. Time-frequency analysis of random signals, inICASSPpp. 1325–1328, 1982.

    Google Scholar 

  34. G. F Boudreaux-Bartels. Time-frequency signal processing algorithms.Analysis and synthesis using Wigner distribution, PhD thesis, Rice University, 1983.

    Google Scholar 

  35. B. Boashash and P. J. Black. An efficient real-time implementation of the Wigner—Ville distributionIEEE Trans.35(11) (1987), 1611–1618.

    Google Scholar 

  36. V. J. Kumar and C. Carroll. Performance of Wigner distribution function based detection methodsOptical Eng.23 (1984), 732–737.

    Google Scholar 

  37. S. Kay and G. F. Boudreaux-Bartels. On the optimality of the Wigner distribution for detectionin Proceedings of the IEEE International Conf on Acoustics Speech and Signal Processingpp. 1263–1265, Tampa, Fl, 1985.

    Google Scholar 

  38. B. Boashash and F. Rodriguez. Recognition of time-varying signals in the time-frequency domain by means of the Wigner distribution, inICASSPpp. 22.5.1–22.5.4, 1984.

    Google Scholar 

  39. B. Boashash and P. J. O’Shea. A methodology for detection and classification of some underwater acoustic signals using time-frequency analysis techniquesIEEE Trans. Acoustics Speech Signal Process.38(11) (1990), 1829–1841.

    Article  Google Scholar 

  40. B. Boashash and P. J. O’Shea.Time-Frequency Analysis: Methods and Applicationschapter on Signal detection using time-frequency analysis, Longman Chesire, London, 1992.

    Google Scholar 

  41. B. Boashash and H. J. Whitehouse. High resolution Wigner-Ville analysis, in11th GRETSI Symposium on Signal Processing and its Applicationspp. 205–208, 1987.

    Google Scholar 

  42. H. J. Whitehouse, B. Boashash, and J. M. Speiser.High-Resolution Techniques in Underwater Acousticschapter on High-resolution processing techniques for temporal and spatial signals, Springer-Verlag, 1990.

    Google Scholar 

  43. H. H. Szu. Two-dimensional optical processing of one-dimensional acoustic dataOptical Eng.21(5) (1982), 804–813.

    Article  Google Scholar 

  44. R. J. Boles and B. Boashash.Time-Frequency Analysis: Methods and Applicationschapter on Applications of the cross Wigner—Ville distribution to seismic surveying, Longman-Chesire, London, 1992.

    Google Scholar 

  45. D. L. Jones and T. W. Parks, A high-resolution data-adaptive time-frequency representationIEEE Trans. Acoustics Speech Signal Process.38(12) (1990), 2127–2135.

    Article  Google Scholar 

  46. N. Marinovic. The Wigner distribution and the ambigutiy function: Generalisations, enhancement, compression and some applications, PhD thesis, City University of New York, 1986.

    Google Scholar 

  47. J. Bertrand and P. Bertrand, Time-frequency representations of broadband signals, inICASSPpp. 2196–2199, 1988.

    Google Scholar 

  48. O. Rioul and P. Flandrin. Time-scale energy distributions: A general class extending wavelet transformsIEEE Trans. Acoustics, Speech Signal Process.(1992), pp. 1746–1757.

    Google Scholar 

  49. R. Altes.Detection, estimation, and classification with spectrogramsJ. Acoust. Soc. Amer.67 (1980), 1232–1246.

    Article  MathSciNet  MATH  Google Scholar 

  50. T. E. Posch. Wavelet transform and time-frequency distributions, inProc. SPIE—Int. Soc. Opt. Engrg.1152 (1989), 477–482.

    Google Scholar 

  51. L. Cohen. Generalised phase space distributionsJ. Math. Phys.7 (1967), 181–186.

    Google Scholar 

  52. B. Barkat and B. Boashash. Higher-Order PWVD and Legendre based time-frequency distribution, inProceedings of the Sixth IEEE Inter. Workshop on Intell. Sig. Proc. and Corn. Systems, Melbourne, 4–6 Nov. 1998.

    Google Scholar 

  53. P. Rao and F. J. Taylor. Artifact reduction in the Wigner distribution, inProc. of the 32nd Midwest Symp. on Circuits and SystemsIllinois, August 1989, pp. 849–852.

    Google Scholar 

  54. A. J. Janssen. Application of the Wigner distribution to harmonic analysis of generalised random processes, PhD thesis, Amdsteram, 1990.

    Google Scholar 

  55. P. Flandrin. Some features of time-frequency representations of multicomponent signals, inProc. of IEEE Inter. Conf on Acoustic Speech and Signal Processing41.B.1.1–41.B.1.4, San Diego, 1984.

    Google Scholar 

  56. H. I. Choi and W. J. Williams. Improved time-frequency representation of multicomponent signals using the exponential kernelsIEEE Trans. Acoustics, Speech Signal Process.37(6) (1989), 862–871.

    Article  Google Scholar 

  57. Y. Zhao, L. E. Atlas, and R. J. Marks II. The use of cone shaped kernels for generalized time-frequency representation of non-stationary signals, IEEE Trans. Acoustics, Speech Signal Process. 38(7) (1990), 1084–1091.

    Article  Google Scholar 

  58. M. AminTime-Frequency Signal Analysis: Methods and Applicationschapter on time-frequency spectrum analysis and estimation for non-stationary random processes, Longman-Chesire, London, 1992.

    Google Scholar 

  59. P. J. Kootsookos, B. C. Lovell, and B. Boashash.A unified approach to the STFT, TDS’s and instantaneous frequencyIEEE Trans. Acoustics, Speech Signal Process.1991.

    Google Scholar 

  60. R. G. Baranuik and D. L. Jones. A radically Gaussian, signal dependent time-frequency representationin Proc. IEEE ICASSPp. 3181–3184, 1991.

    Google Scholar 

  61. G. Jones and B. Boashash. Instantaneous quantities and uncertainty concepts for signal dependent time frequency distributionsin Proc. SPIE1991.

    Google Scholar 

  62. G. Jones and B. Boashash. Generalized instantaneous parameters and window matching in the time-frequency planeIEEE Trans. Signal Process.45(5) (1997), 1264–1275.

    Article  Google Scholar 

  63. B. Barkat and B. Boashash. High-resolution quadratic time-frequency distribution for multicomponent signals analysisIEEE Trans. Signal Process.(1998), (submitted).

    Google Scholar 

  64. P. Rao and F. J. Taylor. Estimation of IF using the discrete Wigner¨CVille distributionElectronics Lett.26 (1990), 246–248.

    Article  Google Scholar 

  65. B. Escudie and P. Flandrin. Positivitü des reprüsentations conjointes en temps et en früquence des signaux d’ ünergie finie; reprüsentation hilbertienne et condition d’observation des signauxin rapport GRETSIpages 2/1–2/7, 1979.

    Google Scholar 

  66. D. König and J. F. Böhme. Wigner-Ville spectral analysis of automative signals captured at knockappl. Signal Process.3 (1996), 54–64.

    Google Scholar 

  67. D. C. Reid, A. M. Zoubir, and B. Boashash. Aircraft flight parameter estimation based on passive acoustic techniques using the polynomial Wigner—Ville distributionJ. Acoust. Soc. Amer. 102(1) (1997), 207–23.

    Article  Google Scholar 

  68. B. Barkat and B. Boashash. Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD: Statistical performance in the presence of additive gaussian noiseIEEE Trans. Signal Process.47(9) (1999).

    Google Scholar 

  69. B. Boashash and A. P. Reilly.Algorithms for Time-Frequency Signal Analysis Chap.7, Longman Chesire, London, 1992.

    Google Scholar 

  70. A. Reilly, G. Frazer, and B. Boashash. Analytic signal generation-tips and trapsIEEE Trans. Signal Process.42 (1994), 3241–3245.

    Article  Google Scholar 

  71. R. Altes. Sonar for generalised target description and its similarity to animal echolocation systems.J. Acoust. Soc. of Amer.59(1) (1976), 97–105.

    Article  MathSciNet  Google Scholar 

  72. A. W. Rihaczek. Principles of High Resolution RadarPeninsula1985.

    Google Scholar 

  73. A. Dziewonski, S. Bloch, and M. Landisman. A technique for the analysis of the transient signalsBull. Seismolog. Soc. Amer.(1969), 427–449.

    Google Scholar 

  74. B. Ferguson. A ground-based narrow-band passive acoustic technique for estimating the altitude and speed of a propellor driven aircraftJ. Acoust. Soc. Amer.92(3) (1992).

    Google Scholar 

  75. S. Peleg and B. Porat. The Cramer—Rao lower bound for signals with constant amplitiude and polynomial phaseIEEE Trans. Signal Process.39(3) (1991), 749–752.

    Article  Google Scholar 

  76. S. Peleg and B. Porat. Estimation and classification of polynomial phase signalsIEEE Trans. Inform. Theory37 (1991), 422–429.

    Article  MathSciNet  Google Scholar 

  77. Z. Faraj and F. Castanie. Polynomial phase signal estimationP. EUSIPCO1992.

    Google Scholar 

  78. B. Boashash and P. J. O’ Shea. Time-varying higher-order spectraProc. SPIE1991.

    Google Scholar 

  79. B. Boashash and B. Ristich. Time-varying higher-order spectra and the reduced Wigner spectrumProc. SPIE1992.

    Google Scholar 

  80. B. Boashash and B. Ristich. Analysis of FM signals affected by Gaussian AM using the reduced Wigner-Ville trispectrum, inProc. ICASSPVol. IV, p. 408–411, Minn. MN, April 1993.

    Google Scholar 

  81. B. Boashash, P. J. O’Shea, and M. J. Arnold. Algorithms for instantaneous frequency estimation: A comparative studyAdvanced Signal Processing Algorithms Architectures and ImplementationsVol. 1348, p. 24–46.Proc. SPIESan Diego, Aug. 1990.

    Google Scholar 

  82. M. Benidir. Characterisation of polynomial functions and application to time-frequency analysisIEEE Trans. Signal Process. 45(5) (1997), 1351–1354.

    Article  Google Scholar 

  83. B. Boashash and B. Ristic. Polynomial time-frequency distributions and time-varying higher-order spectra: application to the analysis of multicomponent FM signal and to the treatment of multiplicative noiseSignal Process.67(1) (1998), 1–23.

    Article  MATH  Google Scholar 

  84. B. Barkat and B. Boashash. Design of higher-order polynomial wigner-ville distributionsIEEE Trans. on Signal Process.47(9) (1999).

    Google Scholar 

  85. B. Barkat. Note on the coefficients precision and selection in the implementation of the PWVD, inProceedings of the Second Workshop on Signal Processing Applicationsp. 131–134, Brisbane, Australia, 4–5 Dec. 1997.

    Google Scholar 

  86. P. O. Amblard and J. L. Lacoume. Construction of fourth-order Cohen’s class: A deductive approach, inProceedings of Int. Sypm. Time-Frequency Time-Scale Analysis1992.

    Google Scholar 

  87. A. Dandawate and G. B. Giannakis. Consistent kth order time-frequency representations for (almost) cyclostationary processesin Proc. Ann. Conference on Information Sciences and Systemsp. 976–984, 1991.

    Google Scholar 

  88. J. R. Fonollosa and C. L. Nikias.Wigner higher-order moment spectra: Definition, properties, computation and application to transient signal analysisIEEE Trans. Signal Process.41(1) (1993), 245–266.

    Article  MATH  Google Scholar 

  89. A. Swami. Third-order Wigner distributions: Defintions and properties, in Proc. ICASSP, p.3081–3084, 1991.

    Google Scholar 

  90. B. Boashash and B. Ristic. Application of cumulant TVHOS to the analysis of composite FM signals in multiplicative and additive noise, inProc. SPIE1993.

    Google Scholar 

  91. R. F. Dwyer. Fourth-order spectra of Gaussian amplitude modulated sinusoidsJ. Acoust. Soc. Amer. 90(2)(1991), 919–926.

    Article  Google Scholar 

  92. A. P. Petropulu.Detection of multiple chirp signals based on a slice of the instantaneous higher-order momentsin IEEE 6th Workshop on Statistical Signal and Array Processingp. 30–33, 1992.

    Chapter  Google Scholar 

  93. L. Stanković. S-class of time-frequency distributionsIEE Proc. Vis. Image Signal Process. 144(2)(1997), 57–64.

    Article  Google Scholar 

  94. L. Stanković. On the realization of the PWVD for multicomponent signalsIEEE Signal Process. Lett. 5(7)(1998), 157–159.

    Article  Google Scholar 

  95. B. Senadji and B. Boashash. A mobile communications application of time-varying higher-order spectra of FM signals affected by multiplicative noise, inProceedings of the International Conference on Information Communications and Signal Processing 3(1997), 1489–92.

    Google Scholar 

  96. B. Barkat, L. J. Stankovic and B. Boashash. Adaptive window in the PWVD for the IF estimation of FM signals in additive Gaussian noise, inICASSP99vol. III, pp. 1317–1320, Phoenix, AZ, March 1999.

    Google Scholar 

  97. V. Katkovnik and L. J. Stankovie. IF estimation using the Wigner distribution with varying and data-driven window lengthIEEE Trans. Signal Process.Sept. 1998.

    Google Scholar 

  98. V. Katkovnik and L J Stankoviü. Periodogram with varying and data-driven window lengthSignal Process.pages 345–358, June 1998.

    Google Scholar 

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Authors
  1. Boualem Boashash
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  2. Braham Barkat
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Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Fl, 32816, USA

    Lokenath Debnath

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Boashash, B., Barkat, B. (2001). Introduction to Time-Frequency Signal Analysis. In: Debnath, L. (eds) Wavelet Transforms and Time-Frequency Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0137-3_11

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  • DOI: https://doi.org/10.1007/978-1-4612-0137-3_11

  • Publisher Name: Birkhäuser, Boston, MA

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