Educational Usage of the Delta Functions as Possible Software Model and Piezoelectric Sensors to Measure Fast Signal in Cracks

Abstract

We review the importance of using a Delta function which can be used as a tool to model instantaneous response signals such as the identification of cracks in piezoelectric materials. We claim that these functions can be part of an interface software-hardware aimed to identify anomalies in large pipes from the fact that the Delta functions under a convolution mechanism having as output a degraded signal that differs notably from the input.A possible application of this formalism would that of the design of algorithms for identifying and measuring cracks properties in metallic pipes by using piezoelectric sensors. We found that the usage of the Delta function would be useful to reconstruct a spectrum indicating the possible locations of cracks within certain range of systematic error. This methodology might also be exploited in the analysis of super fast signals which need to be measure with acceptable resolutions.