The effect of noise upon a method of frequency measurement

The effect of noise upon a method of information transmission and recovery is analyzed. The information is coded as the frequency shift of a carrier. The carrier is assumed to be transmitted over two channels which have phase difference. The recovery of the information is accomplished in a new way by measuring the frequency shift by means of a "coherent cycle counter." A general expression is obtained for the expected frequency measurement of the coherent cycle counter in terms of the signal and noise autocorrelation functions. The percentage bias of the counter is shown to be a function only of the signal-to-noise ratios in the two channels. In the noise-free case, the expected frequency measurement is given by the centroid of the signal power spectrum. When no signal is present the average indicated frequency is zero, thereby effectively cancelling the average effect of the sources of noise in the system. For applications in which the transmitted frequency fluctuates about the carrier or reference frequency, the method is shown to be superior to both an axis crossing counter and an ideal phase differentiator when it is required to operate through zero frequency difference.