Spectral Density and Autocorrelation Functions Associated with Binary Frequency-Shift Keying

The spectral density function, or power spectrum, of a random sequence of signals defines the distribution of average signal power versus frequency. This information is useful in system design because it indicates the frequency band of most importance, the amount of average total power in any frequency interval, and the interference which may result in other systems. It does not tell us how much distortion the signals suffer when the channel does not pass all the frequencies represented, nor does it tell us about important spectral components which may be associated with unlikely but possible specific signal sequences. Keeping these limitations in mind, we still find the spectral density to have merit as a descriptive parameter of the system. Another important function is the autocorrelation, which is the time 2355 2364 THE BEI.L SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1903 domain analog of the spectral density. Because of the Fourier transform relationship between the two functions, either can be used as an auxiliary step in computing the other. The autocorrelation function is useful in its own right in signal analysis and can be made the basis of control operations. The present paper presents results on the spectral density and autocorrelation functions associated with binary frequency modulation systems. There are two general types of operation, which in terms of apparatus may be classified as (a) switching between two oscillators, and (b) changing the frequency of a single oscillator.