## 3 Results and Discussion  
### Time-Frequency Analysis of Velocity Measurements  
The time-domain velocity signals measured by laser vibrometry between 10 and 100 Hz are illustrated in Figure 5 for both tested fruit groups. Each group refers to a set of fruit composed by one sample of each ripening stage. The collected samples were selected by a colorimetry approach that uses CIELab space as a reference. Section 2.1 describes the whole sample classification process. It is important to mention that these were detached from the tree considering a protocol in which the appearance of each would not show defects, and it was as a single fruit, which means not a glomerulus. The ripening stage lines up the graphs and the measured point (P1 and P2) defined for the directions \(e_{1}\) and \(e_{2}\) on the fruits. Different amplitudes of velocity were observed, comparing the three ripening stages at the measured points. This is due to the deformation pattern exhibited by the fruit structure (vibration shape) caused by the kinematics associated with the vibration modes at a specific frequency spectrum when the signals determined at the P1 direction are compared (Figure 5a). The UR1, SMR1, and RP1 graphs  
Figure 4: Experimental setup for modal analysis. (**a**) Lateral view of the experiment. (**b**) Frontal view of sample bonded to the PZT. (**c**) Upper view of the excitation support with piezotransducer and electrodes. (**d**) Representation of the FFT of input voltage. show that unripe fruits had a higher velocity amplitude than the semi-ripe and ripe ones. The colors of each figure represent the ripening stage: green for unripe, orange for semi-ripe, and red for ripe. Figure 6 illustrates the velocity signals measured between 100 and 1000 Hz for both groups of fruits, as Figure 4 shows. In general, comparing the determined signals, it is seen that RP fruits present the highest velocity amplitudes in comparison with SMR and UR. Between fruits of the same ripening stage, the velocity amplitudes differ between P1 and P2. For instance, P1 of UR1 has a lower amplitude than P1 of UR2, and P2 of UR1 tends to be similar to P1 of UR2. P1 of SMR1 has a similar behavior of P1 of SMR 2 and also P2 of SMR1 with P2 of SMR2. As well as the case of semi-ripe fruits, P1 of RP1 and RP2 have higher amplitudes in comparison with P2 of RP1 and RP2. The RMS was computed for the time domain signals of velocity measurements to understand the differences among vibration amplitudes. The mean was also computed for the RMS values determined from the signals that belong to \(e_{1}\) and \(e_{2}\) directions in all the tested fruits. The results for the mean of RMS are summarized in Figure 7, for the selected frequency windows, respectively. Between 10 and 100 Hz, it is observed that the highest value was obtained for the unripe fruits and they decrease sequentially until the ripe ones. In this window, similar values were evidenced between fruits of the same ripening stage, especially the ripe ones that presented the closest values. However, these differences are  
Figure 5: Time domain results of velocity between 10 and 100 Hz in \(e_{1}\) and \(e_{2}\). P1 and P2 measurements for each sample. (**a**) Group 1 (UR1, SMR1, and RP1). (**b**) Group 2 (UR2, SMR2, and RP2). not representative statistically, as illustrated in Figure 7a. On the other hand, between 100 and 1000 Hz, a different trend was observed for the first fruits (UR1, SMR1, and RP1) where the quantities increased from unripe to ripe. However, for the second fruit of each ripening stage, the maximum value was presented in UR2 followed by RP2 and ending with the SMR2 fruit; see Figure 7b. For the time-domain signals, it is not possible to visualize the characteristic mechanical resonances of the fruits due to noise presence.