Correlation Functions and Power Spectra in Variable Networks

The problem considered in this paper is that of establishing a relation between the correlation functions and also the power spectra of the input and output of a linear varying-parameter network (variable network) whose transmission characteristics are random-periodic functions of time. The notion of the correlation function of such a network is introduced and the following theorem is established: The correlation functions of the input and output of a variable network N may formally be regarded as the input and output of a variable network N whose system function is the correlation function of the system function of N. This theorem has many practical applications, particularly in connection with the determination of the correlation functions and power spectra of various random-periodic wave forms.