ABSTRACT
The types of functions can be classified as deterministic, i.e., mathematical expressions can be written that will determine their instantaneous values at any time t. There are, however, a number of physical phenomena that results in nondeterministic data for which future instantaneous values cannot be predicted in a deterministic sense. This chapter discusses the class of stationary ergodic random functions. For the wide-band record, the amplitude, phase, and frequency all vary randomly and an analytical expression is not possible for its instantaneous value. Such functions are encountered in radio noise, jet engine pressure fluctuation, atmospheric turbulence, and so on, and a most likely probability distribution for such records is the Gaussian distribution. The Fourier transform has become the underlying operation for the modern time series analysis. In many of the modern instruments for spectral analysis, the calculation performed is that of determining the amplitude and phase of a given record.
