Conference on Scientic Computing, pp. 188{195 WAVELET TRANSFORM AS POWERFUL TOOL TO ANALYSES OF ACOUSTIC EMISSION SIGNALS

Abstract. The discrete wavelet transformation is a relative new tool to analyse discrete time series. It is similar to the fast Fourier transformation, however, the basically function is not sine and cosine functions. It decomposes an input vector into approximation (low frequency) and detail (high-frequency) levels. Wavelet analysis is a promising set of tools and techniques for signal analysing of seismic shaking, human speech, nancial data, music and many others types of especially non-stationary signals. Key words. wavelet transform, impact-echo method, acoustic emission, de-noising, time-frequency domain AMS subject classications. 15A15, 15A09, 15A23 1. Introduction. Like the fast Fourier transform (FFT), the discrete wavelet transformation (DWT) is a fast, linear operation that operates on a data vector whose length is an integer power of two, transforming it into a numerically dierent vector of the same length. Also like the FFT, the wavelet transformation is invertible and in fact orthogonal- the inverse transformation, when viewed as a big matrix, is simpl