We review the importance of using a Delta function which can be used as a tool to model instantaneous response signals fact that can be useful to be implemented in software hardware interfaces in the analysis of cracks and breaks in metallic pipes by using piezoelectric sensors. Commonly in an output signal derived from a Dirac-Delta convolution the shape appears to follow the one of the input. When the argument of the Dirac-Delta acquires a polynomial form then the resulting output function contains various peaks in different intensities in according to the polynomial structure of the argument. Thus, a possible application of this formalism would that of the design of algorithms for identifying and measuring the cracks in metallic pipes by using piezoelectric sensors. We found that the usage of the Delta function would serve for simulating the reconstructed spectrum in display with a data acquisition much more fast that the conventional ones. This methodology might be exploited in the analysis of super fast signals which need to be measure with acceptable resolutions.