TABLE OF CONTENTS The determination of the frequency bands that contain energy or power in a sample function of a stationary random signal is called spectral analysis. The mode in which this information is presented is an energy or power spectrum. It is the counterpart of the Fourier spectrum for deterministic signals. The shape of the spectrum and the frequency components contain important information about the phenomena being studied. Two applications will be shown before the methodologies are studied. Vibrations are an intrinsic component of rotating machinery. Excessive levels indicate malfunction of some component. Consider Figure 7.1. It is the power spectrum of the vibration measurements from a 1/15 hp electric motor (Noori and Hakimmashhadi, 1988). Vibrations at different frequencies are normal and are created by various moving parts. Some of the frequency components and their sources are indicated in the figure. A malfunction, such as worn-out bearings or loose components, is indicated when its corresponding frequency component has too large a magnitude. Thus the spectrum is a valid tool for machine diagnosis. Another application is in the investigation of the behavior of the smooth muscle of the intestines by measuring the electrical activity, the electrogastrogram (EGG), generated during contraction. The smooth muscle plays an important role in the regulation of gastrointestinal motility and the EGG reflects the mode of muscular contraction. Figure 7.2 shows a measurement from the colon of an experimental dog (Reddy et al., 1987). The activity is irregular. However, when a specific stimuli is...
