Spectral Analysis Techniques Using Wavelets as an Alternative to Fourier Analysis for Transient Dynamic Data
Kenneth R Kimble, Thomas F. Tibbals · 1995
Abstract : Various dynamic data analysis tools for one-dimensional time-domain signals are employed to determine the frequency content of a signal for mechanical analysis. When tied to the fundamental frequency of the various components comprising the machinery being evaluated, this information gives an indication of the state or health of the machine. Current techniques for evaluating dynamic data for potential mechanical problems are primarily centered around the Fast Fourier Transform (FFT) and the Shon Time Fourier Transform (STFT). However, the use of Fourier analysis for frequency component extraction is restricted to bandlimited stationary signals. Because of the stationary requirement, small transients may not be detected due to a smoothing effect of the FFT, or the FFT spectrum may be smeared due to frequency ramping and abrupt incidents or discontinuities in the signal. Various techniques have been employed to overcome the limitations of the FFT for non-stationary data. These techniques include windowed Fourier analysis (including the STFT) and a background in wavelet theory based upon the analyzing function basis approach so that wavelet theory may be contrasted against Fourier analysis. A model signal with stationary and transient characteristics is developed to permit comparisons of various analysis techniques based upon a known analytic signal which resembles a real vibration signal. Some applications of wavelets to other transient signals are also provided.