For fault diagnosis and predictive maintenance of rotating machinery, the phase errors generated by the integration processing of a vibration signal are an essential investigation subject. Phase errors affect the solution of mechanical systems with multiple vibration sources and also the information transmitted through the vibration that is used for fault diagnosis. This work proposes the use of phase plane, recurrence plot (RP), and cross recurrence plot (CRP) to evaluate phase shift error effects on the solution of multiple asynchronous and simple periodic functions, and on the smoothing of a Gaussian peak with white noise. Noisy peaks were smoothed twice with the triangular method and with a different number of points. The analysis of the asynchronous periodic functions and the smoothing indicated that a small phase shift changes the phase plane and the RP pattern. These changes can affect not only the accuracy of machinery fault diagnosis but also prediction for the application of timely maintenance actions.