This chapter details the basic operations required to estimate various properties of random data. The computations to be presented assume that the data are in the form of discrete values representing sample records from stationary (ergodic) random processes. Techniques for the analysis of nonstationary data are presented in Chapter 12, procedures for the computation of Hilbert transforms are developed in Chapter 13, and procedures for the analysis of data representing the response of nonlinear systems are summarized in Chapter 14.
11.1 DATA PREPARATION
As noted in Chapter 10, some random data occur naturally in digital form—for example, neutron emission data and some forms of economic data. In most cases, however, the data originate in analog form and must be converted to digital values with proper concern for (a) the aliasing and quantification problems detailed in Section 10.2 and (b) the data qualification procedures discussed in Section 10.3. Also, the data may be a function of an independent variable other than time—for example, a spatial variable as discussed in Section 5.2.4, Nevertheless, in this chapter, all computations are presented with time as the independent variable (i.e., the data are processed as time-series records) where it is assumed that the actual independent variable for the data record can be made proportional to time. The time parameter in the computed properties of the data can then be replaced by the actual independent variable ...