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Comparison of wavelet transform and Fourier transform applied to analysis of non-stationary processes

Abstract

This article contains a comparison of three data analysis methods’ informativity: wavelet transform, Fourier transform and short-time Fourier transform. This work contains an attempt to find the most sensitive method for the detection of quasiharmonic components in experimental data that have pronounced non-stationary behavior.

Results of high-frequency near-field sounding, IR-spectroscopy and NMR analysis of water, and also model harmonic signal were used as non-stationary processes for analysis.

About the Authors

A. Drozdov
Institute for Analytical Instrumentation Russian Academy of Science
Russian Federation


I. Pomortsev
ITMO University
Russian Federation

St. Petersburg



K. Tyutyukin
St. Petersburg State University, Physical faculty
Russian Federation

St. Petersburg



Y. Baloshin
ITMO University
Russian Federation

St. Petersburg



References

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5. S. Mallat. A Wavelet Tour of Signal Processing. Academic Press, Third Edition, San Diego, California (2008).

6. G. Bachman, L. Narici and E. Beckenstein. Fourier and Wavelet Analysis. Springer-Verlag, Berlin (2000).

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9. S.G. Krantz. A panorama of harmonic analysis. The mathematical association of America, Washington, D.C. (1999).


Review

For citations:


Drozdov A., Pomortsev I., Tyutyukin K., Baloshin Y. Comparison of wavelet transform and Fourier transform applied to analysis of non-stationary processes. Nanosystems: Physics, Chemistry, Mathematics. 2014;5(3):363-373.

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)