This paper provides some results for analyzing relations between frequencies and time of vibration signals. These results have been obtained by studying the properties of wavelet transform, the spectral analysis, the Short-time Fourier transform and by using the toolboxes in the software parked MATLAB. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 24, 2002, No 1 (51 - 64) SOME RESULTS FOR ANALYZIN'G TIME-DEPENDENT FREQUENCIES OF VIBRATION SIGNALS TRAN DUONG TRI Institute of Mechanics, NCST of Vietnam ABSTRACT. This paper provides some results for analyzing relations between frequencies and time of vibration signals. These results have been obtained by studying the properties of wavelet transform, the spectral analysis, the Short-time Fourier transform and by using the toolboxes in the software parked MATLAB. We have created the corresponding PC programs in order to realize algorithms and for the illustration of results by exploring examples. 1. Introduction For analyzing vibrations signal of machine details, constructions. one of the main interested problems is that how to specify the time-frequency relations of that signal. We known, that the Fourier transform allows to establish relations between amplitudes and frequencies only. In last years, the research results of wavelet transform and its applications in the differential domains: functional analysis, signal processing . are interested by several authors [1], [2], [3], [4). However, the applications of the wavelet transform for analysing vibration signals have been little studied. In this paper, we present some initial results in applications of the wavelet transform for analyzing vibration signals. The obtained results had been built in the graphical forms, which are in PC programs. We have written these PC programs in MATLAB language. The main problem is given by the illustrations of relations between frequencies and time of vibration signals 2. A Property of the Wavelet Transform . Definitions Definition 1. A function 'ljJ is defined in the interval R wavelet if the following conditions are satisfied ,P E L 2 (R) and 0 < C;, = ( -oo , +oo) :~ 27' j 1¢ '.~?I' d1'J < oo R 1 J . that is the (2 .1) n where: ~ 1/J(w) = 1 !7L. lim n-+oo y 271" -0 51 .
