Frequency Measurement Techniques

This paper considers the problem of digital frequency measurement of band-limited sampled data signals. The signal is assumed to be a fixed sine wave in noise over the measurement interval. The advent of low-cost A/D converters and the drastic price reductions predicted for IC´s in the near future make techniques of this type appear practical for special-purpose digital hardware as well as a general-purpose computer. The probability density function is determined for frequency measurements based on the nth root of the ratio of the derivative of the signal to the signal itself, or its quadrature component. The results are compared with the instantaneous rate of change of phase technique. In addition, attention is paid to techniques for computing the derivatives of a signal. It is shown that a Lagrange formulation yields an excellent approximation to the first and second derivatives as long as the signal is sampled at no less than twice the Nyquist rate. Finally, it is shown that for a given error, sampling at approximately twice the Nyquist rate minimizes the number of arithmetic operations required per unit time and bandwidth.