Discrete time method for power measurement with nonuniformly sampled signals

The overwhelming majority of the discrete time methods and algorithms for signal/system measurements assume that the digital data at hand are obtained through sampling a continuous time waveform at uniform time intervals. However, in practice, nonuniform sampling occurs in many data acquisition systems due to imperfect sampling timebase, and errors it introduces are sometimes dominating and can not be ignored. In this paper, we investigate the problem of measuring the average power from data samples obtained by nonuniformly sampling a continuous time signal. The relationship between the discrete time expression of the total energy and the continuous time expression is obtained in closed form. The result is applied to the estimation of the average power of sinusoidal signals. It is shown that a simple averaging formula can be used to estimate the average power even with nonuniformly sampled sinusoidal signals if two times of the signal frequency is not an integer multiple of the sampling frequency divided by the sampling offset period, M. It is further demonstrated that a simple averaging method can be used to obtain an accurate estimation even if the frequency condition is not met. Simulations agree with the theoretical predictions