Correlation Functions and Spectra of Phase- and Delay-Modulated Signals

A delay-modulated signal may be regarded as the response of a delay modulator to the carrier of the signal. By using this point of view a general expression for the correlation function of a delay-modulated signal is obtained. This expression is given in an operational form in which the operand is the correlation function of the carrier, and the operator is the correlation function of the delay modulator. The general result is applied to the determination of the correlation function of a delay-modulated signal having a periodic carrier, and, more particularly, to the determination of the correlation function of a phase-modulated signal.