Spectra for a Class of Asynchronous FM Waves

In facsimile data transmission systems, printed or pictorial information is converted into electrical signals by optical means. At any instant the signal corresponds to a definite grey level of the facsimile copy. The resulting electrical wave is an analog signal and can be transmitted as such. In some applications only black-and-white images need be transmitted and therefore the electrical signal may be quantized into only two levels. If more detail is desired, multilevel quantization can be applied. It is possible to model such a quantized signal by considering a random sequence of points on the time (t) axis. At each point a transition may occur in the signal. The value of the signal between transitions is a constant, taking on one of N different values. For the black-and-white case, there are only two permissible values, either +1 or -- 1. The quantized facsimile signal is statistically characterized by specifying the distribution of the points on the t axis and the distribution of the amplitudes between transitions. In this paper we concern ourselves with the spectral density of a carrier wave whose frequency is modulated by quantized facsimile signals. The spectral density is a useful item in the statistical description of such 2149