Accurate Calculation of the Phase Shift Angle of Sinusoidal Signals Using Trapezoidal Rule

In this work, the phase shift angle of a signal is obtained following a procedure that involves carrying out trapezoid rule numerical integration. The two required numerical integrations in this procedure define the tangent function of the phase shift angle. Accurate results (up to the 14th significant figures) are obtained using four equally spaced points (at 0 degrees, 120 degrees, 240 degrees and 360 degrees) on a periodic signal. But the procedure presented here has no limit in the amount of data points that can be used in the numerical integrations. Thus, this procedure can be used to estimate the phase shift angle when data includes noise, using as many points on a period as necessary.