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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
B. Boashash, ed.Time Frequency Signal AnalysisLongman Chesire, Melbourne, 1992.
B. Boashash. Interpreting and estimating the instantaneous frequency of a signal. Part I: Fundamentals.Proceedings of the IEEEpp. 520–538, April, 1992.
B. Boashash. Interpreting and estimating the instantaneous frequency of a signal. Part II: Algorithms Proceedings of the IEEE, 539–569, April, 1992.
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.
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.
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)
D. Gabor. Theory of CommunicationJ. of IEE 93(1946), 429–457.
J. Ville. Theorie et application de la notion de signal analytiqueCables et Transmissions 2A (1)(1948) 61–74.
C. H. Page. Instantaneous power spectraJ. of Appl. Phys. 23(1)(1953), 103–106.
C. Turner. On the concept of an instantaneous power spectra and its relation to the autocorrelation functionJ. of Appl. Phys. 25(1954), 1347–1351.
M. Levin. Instantaneous spectra and ambigutiy functionIEEE Trans. Inform. Theory 13(1967), 95–97.
A. Rihaczek. Signal energy distribution in time and frequencyIEEE Trans. Inform. Theory 14(3)(1968), 369–374.
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.
T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution—Part 1Phillips J. Res. 35(1980), 217–250.
T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution— Part 2Phillips J. Res. 35(1980), 276–300.
T. A. C. M. Classen and W. F. G. Mecklenbrauker. The Wigner distribution—Part 3Phillips J. Res. 35(1980), 372–389.
B. Boashash, P. Flandrin, B. Escudie, and J. Grea.Positivity of time-frequency distributions C. R. Acad. Sci. Paris(1979).
B. Boashash. Wigner analysis of time-varyirig signals—Its application in seismic prospecting, inProc. EUSIPCOpp. 703–706, 1983.
B. Boashash. Representation conjointe en temps et en frequence des signaux d’energie finie, Technical Report 373 78, Elf-Acquitaine Research Publication, 1978.
J. Jeong and W. J. Williams, Kernel design for reduced interference distributionsIEEE Trans. Signal Process. 40(2)(1992), 402–412.
B. Ristic. Signal dependent and higher-order time-frequency analysis, PhD thesis, Signal Processing Research Centre, Queensland University of Technology, Australia, 1995.
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.
G. Jones. Time-frequency analysis and the analysis of multicomponent signals, PhD thesis, Queensland University of Technology, 1992.
J. Kay and R. Lerner.Lectures in Communications TheoryMcGraw-Hill, New York, 1961.
C. Helstrom. An expansion of a signal into Gaussian elementary signalsIEEE Trans. Inform. Theory 13(1966), 344–345.
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.
L. Cohen. Time-frequency distributions—A reviewProc. IEEE 77(1989), 941–981.
B. Boashash. Note on the use of the Wigner distributionIEEE Trans. Acoustics, Speech Signal Process. 36(9)(1988), 1518–1521.
E. P. Wigner. On the quantum correction for thermodynamic equilibriumPhys. Rev. 40(1932), 748–759.
B. Boashash. Representation temps-frequence. PhD thesis, Dipl. de Docteur-Ingenieur these, University of Grenoble, 1982.
B. Boashash. Note d’information sur la representation des signaux dans le domaine temps-frequence, Technical Report, 135 81, Elf-Aquitaine Research Publication, 1981.
W. Martin. Time-frequency analysis of random signals, inICASSPpp. 1325–1328, 1982.
G. F Boudreaux-Bartels. Time-frequency signal processing algorithms.Analysis and synthesis using Wigner distribution, PhD thesis, Rice University, 1983.
B. Boashash and P. J. Black. An efficient real-time implementation of the Wigner—Ville distributionIEEE Trans.35(11) (1987), 1611–1618.
V. J. Kumar and C. Carroll. Performance of Wigner distribution function based detection methodsOptical Eng.23 (1984), 732–737.
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.
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.
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.
B. Boashash and P. J. O’Shea.Time-Frequency Analysis: Methods and Applicationschapter on Signal detection using time-frequency analysis, Longman Chesire, London, 1992.
B. Boashash and H. J. Whitehouse. High resolution Wigner-Ville analysis, in11th GRETSI Symposium on Signal Processing and its Applicationspp. 205–208, 1987.
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.
H. H. Szu. Two-dimensional optical processing of one-dimensional acoustic dataOptical Eng.21(5) (1982), 804–813.
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.
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.
N. Marinovic. The Wigner distribution and the ambigutiy function: Generalisations, enhancement, compression and some applications, PhD thesis, City University of New York, 1986.
J. Bertrand and P. Bertrand, Time-frequency representations of broadband signals, inICASSPpp. 2196–2199, 1988.
O. Rioul and P. Flandrin. Time-scale energy distributions: A general class extending wavelet transformsIEEE Trans. Acoustics, Speech Signal Process.(1992), pp. 1746–1757.
R. Altes.Detection, estimation, and classification with spectrogramsJ. Acoust. Soc. Amer.67 (1980), 1232–1246.
T. E. Posch. Wavelet transform and time-frequency distributions, inProc. SPIE—Int. Soc. Opt. Engrg.1152 (1989), 477–482.
L. Cohen. Generalised phase space distributionsJ. Math. Phys.7 (1967), 181–186.
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.
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.
A. J. Janssen. Application of the Wigner distribution to harmonic analysis of generalised random processes, PhD thesis, Amdsteram, 1990.
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.
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.
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.
M. AminTime-Frequency Signal Analysis: Methods and Applicationschapter on time-frequency spectrum analysis and estimation for non-stationary random processes, Longman-Chesire, London, 1992.
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.
R. G. Baranuik and D. L. Jones. A radically Gaussian, signal dependent time-frequency representationin Proc. IEEE ICASSPp. 3181–3184, 1991.
G. Jones and B. Boashash. Instantaneous quantities and uncertainty concepts for signal dependent time frequency distributionsin Proc. SPIE1991.
G. Jones and B. Boashash. Generalized instantaneous parameters and window matching in the time-frequency planeIEEE Trans. Signal Process.45(5) (1997), 1264–1275.
B. Barkat and B. Boashash. High-resolution quadratic time-frequency distribution for multicomponent signals analysisIEEE Trans. Signal Process.(1998), (submitted).
P. Rao and F. J. Taylor. Estimation of IF using the discrete Wigner¨CVille distributionElectronics Lett.26 (1990), 246–248.
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.
D. König and J. F. Böhme. Wigner-Ville spectral analysis of automative signals captured at knockappl. Signal Process.3 (1996), 54–64.
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.
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).
B. Boashash and A. P. Reilly.Algorithms for Time-Frequency Signal Analysis Chap.7, Longman Chesire, London, 1992.
A. Reilly, G. Frazer, and B. Boashash. Analytic signal generation-tips and trapsIEEE Trans. Signal Process.42 (1994), 3241–3245.
R. Altes. Sonar for generalised target description and its similarity to animal echolocation systems.J. Acoust. Soc. of Amer.59(1) (1976), 97–105.
A. W. Rihaczek. Principles of High Resolution RadarPeninsula1985.
A. Dziewonski, S. Bloch, and M. Landisman. A technique for the analysis of the transient signalsBull. Seismolog. Soc. Amer.(1969), 427–449.
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).
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.
S. Peleg and B. Porat. Estimation and classification of polynomial phase signalsIEEE Trans. Inform. Theory37 (1991), 422–429.
Z. Faraj and F. Castanie. Polynomial phase signal estimationP. EUSIPCO1992.
B. Boashash and P. J. O’ Shea. Time-varying higher-order spectraProc. SPIE1991.
B. Boashash and B. Ristich. Time-varying higher-order spectra and the reduced Wigner spectrumProc. SPIE1992.
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.
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.
M. Benidir. Characterisation of polynomial functions and application to time-frequency analysisIEEE Trans. Signal Process. 45(5) (1997), 1351–1354.
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.
B. Barkat and B. Boashash. Design of higher-order polynomial wigner-ville distributionsIEEE Trans. on Signal Process.47(9) (1999).
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.
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.
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.
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.
A. Swami. Third-order Wigner distributions: Defintions and properties, in Proc. ICASSP, p.3081–3084, 1991.
B. Boashash and B. Ristic. Application of cumulant TVHOS to the analysis of composite FM signals in multiplicative and additive noise, inProc. SPIE1993.
R. F. Dwyer. Fourth-order spectra of Gaussian amplitude modulated sinusoidsJ. Acoust. Soc. Amer. 90(2)(1991), 919–926.
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.
L. Stanković. S-class of time-frequency distributionsIEE Proc. Vis. Image Signal Process. 144(2)(1997), 57–64.
L. Stanković. On the realization of the PWVD for multicomponent signalsIEEE Signal Process. Lett. 5(7)(1998), 157–159.
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.
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.
V. Katkovnik and L. J. Stankovie. IF estimation using the Wigner distribution with varying and data-driven window lengthIEEE Trans. Signal Process.Sept. 1998.
V. Katkovnik and L J Stankoviü. Periodogram with varying and data-driven window lengthSignal Process.pages 345–358, June 1998.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0137-3_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6629-7
Online ISBN: 978-1-4612-0137-3
eBook Packages: Springer Book Archive