Measurement of the period of nonsinusoidal signals with a dc component

Abstract

In digital signal processing it is frequently necessary to measure the frequency or period of the investigated signals. Two methods are known for period measurements. The first (integrating) method is based on the fact that the integral of a periodic signal not containing a de component is equal to zero during a time that is equal or is a multiple of the signal period [1, 2]. This method is characterized by high noise immunity. Unfortunately, the method is only suitable for measuring periods of signals without a de component.The second method relies on the fact that at any time the instantaneous value of a harmonic signal and the value of its derivative at this instant are repeated at time intervals equal to the signal period irrespoctive of whether the signal has a de component or not [3, 4]. The period of a signal containing a de component can thus be determined. A limitation of this method is its low noise immunity. Noise and higher harmonic components may cause considerable errors since, even if the sign of its derivative is considered, the one and the same signal value may recur more than once during one period. Noise immunity of this method can be improved by analyzing the results of several measurements taken over several periods, but this increases measurement time considerably.The proposed method of signal period measurement retains the advantage of both methods and is free of their limitations. The method is based on the comparison of two integrals of a harmonic signal with a de component taken at time intervals t during a fixed time interval t o. As shown below, these integrals are equal to each other twice while the time varies from 0 to the signal period T, the second time occurring when t = T. Thus, the equationshould turn into an identity at certain t = t t < T and t = h = T, where U m, co, and ~o are the signal amplitude, frequency, and phase respectively, and U 0 is the de component. Consequently, the signal period duration can be found from the time t 2 when the two integrals are equal. Let us show that integrals of a harmonic function with a de component, taken at a current time interval t during a fixed time t o , are equal to each other twice during one signal period. Let F (tot ) = A (to)--B (t o, t),(1)