There have been many different definitions of energy functions as the second statistics of a signal. In this paper, using the higher order differential energy function, we propose an algorithm separating the amplitude and frequency components in a discrete sinusoidal signal. The proposed amplitude and frequency estimation methods have less computational requirement than the existing methods. It also shows large computational advantage over the root mean square (RMS) calculation of a signal. The proposed methods can be used in the detection of abnormal events in signals on the power line. Computer simulations show that proposed frequency estimation method can detect the presence of voltage increase or decrease for a short period of time. Also, the proposed estimation methods have been compared with existing methods in terms of estimation error variance.