This paper presents an interpretation of the results of the Pulse-echo methods (Radar Impact-Echo, Ultrasonic Impulse-echo) and simulation of wave propagation for testing concrete specimens with metal ducts given in [1-15], in terms of the invariance properties of PTF (Practical Test Function) model for asymmetrical pulses presented and developed in [20] and [26]. The interpreted results include various aspects of the pulse echo method (previously published by Krause, Maierhofer, Wiggenhauser, Barmann, Langenberg, Frielinghaus, Krautkramer, Neisecke, Wollbold, Schickert) as: radar: propagation, reflection and scattering of electromagnetic pulses; impact echo: propagation, reflection and scattering of elastic waves after mechanical impact; ultrasonic pulse echo: propagation and dispersion of sound waves after indication with ultrasonic transducers. The interpretation of the above results with the help of the PTF model for asymmetrical functions revealed the compatibility between the first and second order therms representation of a sharp pulse-defined as a practical test function- and some of the experimental results. As a possible application, is mentioned phase detection by multiplying the alternating input signal with an assymetrical function and integration of the resulting function for more robust results than the one presented in [27]. The second part of the paper presents the a heuristic algorithm for generating asymmetrical practical test functions (that could be used to describe impact echo phenomena for the elastic waves in various materials, including concrete) using MATLAB procedures some possibilities for obtaining asymmetrical pulses as related to this middle of the working interval using the derivative of such symmetrical pulse for certain diferential equations corresponding to second order systems (with unity-step input and for an input represented by a gaussian pulse).
