Short-Time Frequency Measurement of Narrow-Band Random Signals by Means of a Zero Counting Process

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Abstract
Any instrumentation for measuring the mean frequency of a narrow-band random signal presents an output quantity which inherently fluctuates about that value which represents the true mean frequency, due to the finite measuring time. In comparing the accuracy of various instrumentations for short-time frequency measurement a useful figure of merit is variance of the output/(sensitivity)2. In this paper the figure of merit is obtained for an instrumentation which measures frequency by determining the average number of zero crossings of the signal in a short time. The significant problem is the determination of the mean square number of zeros of a random function in time T. The general result is presented in the form of an integral. For an assumed Gaussian power spectrum the integral is integrated graphically to obtain a figure of merit which is compared with previously published figures of merit of an autocorrelator and frequency discriminator.

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