TABLE OF CONTENTS Knowledge of the cyclic or oscillating activity in various physical and biological phenomena and in engineering systems has been recognized as essential information for many decades. In fact, interest in determining sinusoidal components in measured data through modeling began at least several centuries ago and was known as harmonic decomposition. The formal development of Fourier analysis dates back to the beginning of the eighteenth century and the creative work of Jean Fourier who first developed the mathematical theory that enabled the determination of the frequency composition of mathematically expressible waveforms. This theory is called the Fourier transform and has become widely used in engineering and science. During the middle of the nineteenth century, numerical techniques were developed to determine the harmonic content of measured signals. Bloomfield (1976) summarizes a short history of these developments.
One of the older phenomena that has been studied are the changes in the intensity of light emitted from a variable star. A portion of such a signal is plotted in Figure 3.1. It is oscillatory with a period of approximately 25 days. Astronomers theorized that knowledge of the frequency content of this light variation could yield not only general astronomical knowledge but also information about the star's creation (Whittaker and Robinson, 1967). Another phenomena that is usually recognized as oscillatory in nature is vibration. Accelerometers are used to measure the intensity and the frequencies of vibration, and testing them is necessary in order to determine their accuracy. Figure 3.2 shows the...
