## 2 Materials and Methods
### Algorithm Implemented  
The implemented software is depicted in Figure 6. The audio sampling frequency was set to 200 kHz, and considering that the analyzed signals are in the band up to 10 kHz, the signal is oversampled, in order to avoid aliasing problems. The force-sensor sampling frequency was set to 500 kHz to acquire a sufficient number of points to measure properly the impact-time. The depth of quantization is 10 bit. As already stated in the introduction, the concept underlying the algorithm is to establish a test point at which there is certainty: this point can, for example, be adherent with certainty. The restorer, based on his experience and professionalism, establishes the test point; with respect to this point all the other points will be compared, and the result will tell if the point under examination is similar to the one taken as test-point or is definitely dissimilar from it, using both the information coming from the impact-time measurement and the correlation index that is calculated by comparing the audio recorded by the test point and the point being measured. The number of audio samples is set to 512 which is a good compromise between the memory occupation and the fidelity of the recorded signal. The data frame is 2.56 ms long and is suitably windowed considering the references introduced by the signal coming from the force sensor. In fact, as can be seen in Figure 7a, the audio signal to be analyzed is triggered by the force sensor signal. Furthermore, even considering the dead-time due to the distance between the microphone and the impact point of the hitting device (1 cm, thus about 30 \(\upmu\)s), the remaining acquisition time is sufficient to consider the main part of the audio signal. Figure 7 shows an acquisition of an audio signal obtained hitting the surface and the relative signal of the force sensor (both appropriately scaled). The figure shows the starting point of the 512-sample window which will then be analyzed by the cross-correlation index extraction software. The signal is acquired starting from 12 samples before the maximum of the force sensor signal and ends after the acquisition of 512 samples. Obviously the acquired signal is wider, and the window is applied after the acquisition. Figure 5: The 32-bit microcontroller unit: (**a**) the Fishino32 board; (**b**) the shield board used in the paper. Furthermore, Figure 7b shows two acquisitions of the signal due to the force sensor. As mentioned, the presence of defects will decrease the local stiffness of the structure and produce a wider force-time pulse or shows a longer contact time. The test surface is analyzed by comparing the contact time or determining the deviation of the force-time pulse width from the nominal width obtained from a reference undamaged surface. Hence, the sound of a rigid area will give a lower reading whereas a damaged area will give a higher reading of the impact-time. First, the test signal is memorized by the central processing unit (CPU) while tapping a part of the test-object apparently in a good state of conservation and the impact time T\({}_{0}\) of the part is memorized as the standard value. Then the test-object is scanned with the hammer and, when the hammer hits a detached part, the impact time T at that moment is compared with the memorized standard value. An  
Figure 6: The flow chart of the implemented software (audio section). Figure 7: An example of the acquired audio signal and the relative force sensor signal. In **(a)** is showed the window of the samples that will be calculated by the cross-correlation algorithm. In **(b)** the comparison between the contact-time of a rigid area (blue fit) vs. a damaged area (red fit). appropriate ratio of the relationships between the two time-durations measures in a simple way the state of detachment/no-detachment of the measured object.