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Joint time-frequency and wavelet analysis - an introduction

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Języki publikacji
EN
Abstrakty
EN
A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.
Rocznik
Strony
741--758
Opis fizyczny
Bibliogr. 28 poz., rys., wykr., wzory
Twórcy
autor
  • Warsaw University of Technology, Institute of the Theory of Electrical Engineering, Measurement and Information Systems, Koszykowa 75, 00-662 Warsaw, Poland
  • Warsaw University of Technology, Institute of the Theory of Electrical Engineering, Measurement and Information Systems, Koszykowa 75, 00-662 Warsaw, Poland
autor
  • Warsaw University of Technology, Institute of the Theory of Electrical Engineering, Measurement and Information Systems, Koszykowa 75, 00-662 Warsaw, Poland
Bibliografia
  • [1] Boashash, B. (2003). Time-Frequency Signal Analysis and Processing: A Comprehensive Reference. Elsevier Science, Oxford.
  • [2] Time-Frequency Toolbox for use with MATLAB. (1996). CNRS (France) and Rice University (USA).
  • [3] Mallat, S. (1989). A Theory of Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7, 674-693.
  • [4] Qian, S. (2002). Introduction to Time-Frequency and Wavelet Transforms, Prentice Hall Professional Technical Reference.
  • [5] Mallat, S. (1998). A wavelet Tour of Signal Processing, Academic Press.
  • [6] Boualem Boashash, B. (2003). Time Frequency Analysis. Gulf Professional Publishing.
  • [7] Qian, S., Chen, D. (1999). Joint time-frequency analysis. IEEE Signal Processing Magazine, 2, 52-67.
  • [8] Nievergelt, Y. (2013). Wavelets Made Easy , Springer.
  • [9] Goswami, J. C., Chan, A. K. (1999). Fundamentals of wavelets - Theory, Algorithms and Applications. John Wiley & Sons Inc. New York.
  • [10] Signal Processing Toolset User Manual. (2001). National Instruments.
  • [11] Burrus, C. S., Gopinath, R. A., Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice Hall Inc.
  • [12] Qian, S., Chen, D. (1996). Joint Time-Frequency Analysis. Englewood Cliffs, N.J., Prentice-Hall.
  • [13] Cohen, L. (1995). Time-Frequency Analysis. Prentice-Hall, New York.
  • [14] Cohen, L., Loughlin, P. (1998). Recent Developments in Time-Frequency Analysis. Springer.
  • [15] Heil, C., David, F., Walnut, D.F. (2000). Fundamental Papers in Wavelet Theory. Princeton University Press.
  • [16] Meyer, Y., Ryan, R. D. (1993). Wavelets: Algorithms & Applications. Society for Industrial and Applied Mathematics.
  • [17] Kaiser, G. (1999). A Friendly Guide to Wavelets. C. Valens.
  • [18] Cohen, A. (2003). Numerical Analysis of Wavelet Methods. North Holland.
  • [19] Van den Berg, J. C. (2004). Wavelets in Physics. Cambridge University Press.
  • [20] Daubechies, I. (1992). Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics.
  • [21] Wavelet Toolbox for use with Matlab. (2012). Mathworks Inc.
  • [22] Flandrin, P. (1999). Time-frequency/Time-Scale Analysis, Wavelet Analysis and its Applications, 10, Academic Press, San Diego.
  • [23] Koornwinder, T. H. (1993). Wavelets: An Elementary Treatment of Theory and Applications. World Scientific.
  • [24] Mecklenbrauker, W., Hlawatsch, F. (1997). The Wigner distribution: theory and applications in signal processing. Elsevier.
  • [25] Papandreou-Suppappola, A. (2010). Applications in Time-Frequency Signal Processing. Taylor & Francis.
  • [26] Zieliński, T. P. (2009). Digital signal processing. From theory to implementations. WKŁ.
  • [27] Jaffard, S., Meyer, Y., Ryan, R. D. (2001). Wavelets, Tools for Science and Technology. Society for Industrial and Applied Mathematics.
  • [28] Boualem Boashash, B. (1992). Time-frequency signal analysis-methods and applications. Longman Cheshire.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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