The article presented some promising patents and other correlated literature on wavelet functions for rejecting spurious values (gross errors) in a continuous digital sequence of measured values. Moreover, the paper concentrates its attention on an innovative invention which addresses Gross Error Detection using uni-variate signal-based approaches. The developed algorithm is totally general and it is present in some industrial software platforms to detect sensor outliers. Furthermore, it is currently integrated in the inferential modelling platform of the unit responsible for Advanced Control and Simulation Solutions within ABB's (Asea Brown Boveri) industry division. Experimental results using sensor measurements of temperature, pressure and Enthalpy in a Distillation Column are presented in the paper. One of the goals of this paper is to show the possibility to include the wavelet algorithms also for data reconciliations and authentications in modern communication systems such as wireless communication ones. Wavelet packets seem particularly suitable in such kind of applications because they could also be utilized in the compression data system. Therefore, using wavelet packets a more compact and integrated structure of the whole data transmission and data reconciliation system seems to be possible.