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Reseach Article

Significance of Cohen's Class for Time Frequency Analysis of Signals

by Azeemsha Thacham Poyil, Nasimudeen K.m, Sultan Aljahdali
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 72 - Number 12
Year of Publication: 2013
Authors: Azeemsha Thacham Poyil, Nasimudeen K.m, Sultan Aljahdali
10.5120/12543-8960

Azeemsha Thacham Poyil, Nasimudeen K.m, Sultan Aljahdali . Significance of Cohen's Class for Time Frequency Analysis of Signals. International Journal of Computer Applications. 72, 12 ( June 2013), 1-8. DOI=10.5120/12543-8960

@article{ 10.5120/12543-8960,
author = { Azeemsha Thacham Poyil, Nasimudeen K.m, Sultan Aljahdali },
title = { Significance of Cohen's Class for Time Frequency Analysis of Signals },
journal = { International Journal of Computer Applications },
issue_date = { June 2013 },
volume = { 72 },
number = { 12 },
month = { June },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume72/number12/12543-8960/ },
doi = { 10.5120/12543-8960 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:37:42.397345+05:30
%A Azeemsha Thacham Poyil
%A Nasimudeen K.m
%A Sultan Aljahdali
%T Significance of Cohen's Class for Time Frequency Analysis of Signals
%J International Journal of Computer Applications
%@ 0975-8887
%V 72
%N 12
%P 1-8
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, a study of quadratic transformations under Cohen's class is presented, to see the variations in resolution for performing time-frequency analysis of signals. The study concentrated on the analysis of linear chirp signals and non-stationary signals in presence of noise as well as without noise. The resolutions based on Wavelet Transform, Short Time Fourier Transform are analysed. The effects of widow length, wavelet scale and presence of noise are researched and analyzed against the performance of different time-frequency representations. The Cohen's class is a class of time-frequency quadratic energy distributions which are covariant by translations in time and in frequency. This important property by the members of Cohen's class makes those representations suitable for the analysis and detection of linear as well as transient signals. Spectrogram, the squared modulus of Short Time Fourier Transform is considered to be an element of Cohen's class since it is quadratic and also co-variant in time and frequency. Wigner Ville Distribution is another member of Cohen's class which can be extended to many other variants by changing the kernel functions used for cross-term reductions. The trade-off in the time-frequency localization are studied and demonstrated with the help of different plots. The result of this study can be applied to enhance the detection and analysis of signals and to develop efficient algorithms in medical diagnosis as well as defense applications.

References
  1. François Auger, Patrick Flandrin, Paulo Gonçalvès, Olivier Lemoine, Tutorial - Time Frequency Toolbox for use with MATLAB, 1996
  2. Azeemsha Thacham Poyil, Shadiya Alingal Meethal, "Cross-term Reduction Using Wigner Hough Transform and Back Estimation", IEEE Explore, Issue date 23-25 Aug. 2012
  3. N. Zaric, N. Lekic, and S. Stankovic, "An implementation of the L-estimate distributions for analysis of signals in heavy-tailed noise," IEEE Transactions on Circuits and Systems II, Vol. 58, No. 7, July 2011, pp. 427-431
  4. G. Yu; S. Mallat, and E. Bacry, "Audio denoising by time-frequency block thresholding," IEEE Transactions on Signal Processing, Vol. 56, No. 5, May 2008, pp. 1830-1839.
  5. Y. S. Wei and S. S. Tan, "Signal decomposition of HF radar maneuvering targets by using S2-method with clutter rejection,"Journal of Systems Engineering and Electronics, Vol. 23, No. 2, April 2012, pp. 167 - 172.
  6. Y. C. Jiang, "Generalized time–frequency distributions for multi-component polynomial phase signals,"Signal Processing, Vol. 88, No. 4, April 2008, pp. 984–1001.
  7. Yictor Sucic and Boualem Boashash, "Optimization Algorithm for Selecting Quadratic Time-frequency Distributions: Performance Results and Calibration" International Symposium on Signal Processing and its Applications (ISSPA), Kuala Lumpur, Malaysia, 2001
  8. Daniel Mark Rosser, "Time-Frequency Analysis of a Noisy Career Signal", Naval Post Graduate School Monterey, California, 1996
  9. Boualem Boashash, "Time-Frequency Signal Analysis and Processing – A Comprehensive Reference", Queensland University of Technology, Brisbane, Australia, 2003
  10. Alfred Hanssen, and Louis L. Scharf, "A Theory of Polyspectra for Nonstationary Stochastic Processes", IEEE Transactions On Signal Processing, Vol. 51, No. 5, 2003
  11. Juan D Mart´?nez-Vargas, Juan I Godino-Llorente, and German Castellanos-Dominguez, "Time–frequency based feature selection for discrimination of non-stationary biosignals", EURASIP 2012
  12. Ervin Sejdic, Igor Djurovic and Jin Jiang, "Time-Frequency Feature Representation Using Energy Concentration: An Overview of Recent Advances", ScienceDirect, Digital Signal Processing 19 (2009) 153–183
  13. H. Zou, Q. Dai, R. Wang, and Y. Li, "Parametric TFR via windowed exponential frequency modulated atoms," IEEE Signal Processing Letters, Vol. 8, No. 5, May 2001,
  14. Hongxing Zou, Dianjun Wang, Xianda Zhang, Yanda Li, "Nonnegative time–frequency distributions for parametric time–frequency representations using semi-af?ne transformation group", Signal Processing 85 (2005)
  15. Time-series analysis in marine science and applications for industry, 17– 21 September 2012 – Logonna-Daoulas, France
  16. Jun Jason Zhang, Antonia Papandreou-Suppappola, Bertrand Gottin, and Cornel Ioana, "Time-Frequency Characterization and Receiver Waveform Design for Shallow Water Environments", IEEE Transactions On Signal Processing, Vol. 57, No. 8, August 2009
  17. B. Zhang and S. Sato, "A time-frequency distribution of Cohen's class with a compound kernel and its application to speech signal processing," IEEE Transactions on Signal Processing, Vol. 42, No. 1, Jan. 1994, pp. 54-64.
Index Terms

Computer Science
Information Sciences

Keywords

Wavelet Transform (WT) Scalogram Short Time Fourier Transform (STFT) Fast Fourier Transform (FFT) Wigner Ville Distribution (WVD) Cohen's Class Spectrogram