The well-known formulas relating power spectral densities of a bandpass process and its low-pass representors in Rice's representation are generalized to accommodate cyclostationary processes, which can be more appropriate than stationary processes as models for modulated signals. It is explained that improper phase-randomization methods for stationarizing cyclostationary processes can yield misleading formulas for power spectral densities in Rice's representation. In addition, the relationships among the spectral correlation functions for a cyclostationary bandpass process and its cyclostationary low-pass representors are derived.

The common practice of applying the theory of stationary stochastic processes to a cyclostationary process by introducing random phase(s) into the probabilistic model in order to stationarize the process can lead to erroneous results, such as incorrect formulas for power spectral density. This is illustrated by showing that commonly used formulas for signals that have undergone frequency conversion or time sampling can be incorrect. The source of error is shown to be inappropriate phase-randomization procedures. The correct procedure is described, and corrected formulas are given. The problem is further illustrated by showing that commonly used resolution and reliability (mean and variance) formulas for spectrum analyzers must be corrected for cyclostationary signals. It is explained that all corrections to formulas reflect the effects of spectral correlation. These effects are inappropriately averaged out by inappropriate phase-randomization procedures. It is further explained that these inappropriate procedures destroy the important property of ergodicity of the probabilistic model.

The importance of the concept of cyclostationarity in design and analysis of signal detectors, synchronizers, and extractors in communication systems is briefly discussed, and the central role of spectral correlation, in the characterization of random processes that are cyclostationary in the wide sense, is explained. A spectral correlation function that is a generalization of the power spectral density function is described, and a corresponding generalization of the Wiener-Khinchine relation and several other fundamental spectral correlation relations also are described. Explicit formulas for the spectral correlation function for various types of analog-modulated signals are derived. This includes pulse and carrier amplitude modulation, quadrature amplitude carrier modulation, and phase and frequency carrier modulation. To illustrate the differing spectral correlation characteristics of different modulation types, the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane.