<title>Signal processing in ultrasonic NDE using time-frequency representations</title>

Abstract

Signal processing has been used in the ultrasonic nondestructive evaluation (NDE) of materials for a number of years. The time domain analysis of NDE signals includes signal enhancement, deconvolution, matched filtering, etc. and the results can often be linked to physical parameters. Frequency (Fourier) analysis of NDE singals provides information about the major frequency components which may be closely related to the geometry of hidden defects, material properties, etc.It is clear that the use of frequency domain or time domain information alone is not adequate for effective NDE. Recent advances in digital signal processing have resulted in new and effective approaches to joint time-frequency representations that provide more information from the data which may be useful for defect characterization and classffication. Among all time-frequency analysis methods, both Wigner distributions and wavelet transforms have been considered for use in ultrasonic NDE. However the full potential of time-frequency representation in ultrasonic NDE is yet to be explored. In this paper, a fundamental analysis of time frequency representations is briefly presented. Several application areas of the timefrequency representation in ultrasonic NDE including geometrical defect discrimination, NDE ofbonded materials, sizing problem with geometrical defects, and waveform decomposition are examined in detail. The fundamental time-frequency analysis is the short-time Fourier transform. A signal function x(t) issegmented into a number of sections by using a window function. The STFT is defined as (see e.g. [1]) STFT(t,f) = fx(t)g*(t _ t)e2dt(1) where g(t) is the window function. The asterisk '*' denotes the complex conjugate. The plane formed by the twodimensional function STFT(t,J) is called the complex spectrogram. The square value of the magnitude of STF7(t,j) is termed spectrogram. The inverse STFT can be obtained straightforwardly by taking the inverse Fourier transform. Taking the inverse Fourier transform of Eq. 1, we have : STFT('c, f)e32'df = xQ)g * (tLet t = t and move g(.) to the other side of equality sign.x(t) = J STFT(t f)e2'df (2) g (0) if the window function g(t) satisified the unity energy constraint, j'g(t)2dt = 1 , the inverse STFT can also be derived by taking the inverse Fourier transform of the windowed STFT(t,J). The derivation is omitted here.Equations 1 and 2 together are called STFT pairs. The sampled version STFT pairs are given in Eqs. 3 and 4, where T and F are the sampling interval in time and frequency, respectively. STFT(mT, nF) = f x(t)g*(t -mT'2tdt (3) x(t) = STFT(mT, nF)g(t -mT)e32t (4) SPIE Vol. 2921 • 0277-786X197/$lO.OO 319 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/23/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx