## 4 Discussion  
Measurements carried out using a robot-equipped stand supported the claim that the re-excitation of a guitar string produces a sound that is different from a single excitation, or its first excitation. The observed changes in spectra (Figure 11) exceeded 10 dB in some frequency bands, which was clearly perceivable by the human ear [18,19]. The spectral changes depend on the re-excitation delay (Figure 7), so a series of otherwise-similar guitar string plucks (with regards to plucking position, angle, or amplitude) will vary due to the state of the string at the moment of plucking, and this variability can be detected by human hearing. For better realism, sound synthesis needs to replicate this behaviour. The first simulation model (L1 and S1) took into consideration the fact that a string is vibrating during re-excitation and that secondary excitation is imposed on that state. Apart from that, no previous contact with the spectrum nearing a string was considered. However, the spectrogram of the robot measurement (Figure 12) showed that, just before the re-excitation, the string received partial contact with the moving plectrum, producing two auditory effects: ringing and damping. The latter could be observed by the harmonics  
Figure 12: Spectrograms of slow re-excitation for robot measurements (**top**) and both simulations (**middle** and **bottom** plot). becoming less distinct and by so-called pitch-glides--slight and gradual frequency changes in some harmonics. Therefore, the first model was insufficient to replicate these phenomena. What was also interesting is that re-excitation after a single fundamental string period (12 ms) did not produce the same spectrum, contrary to the prediction of the simple model (Figures 10 and 11). The spectral changes caused by re-excitation were larger and more complex, and required a better model to be at least partially reproduced. The second simulation model (L2 and S2) introduced contact between a plucking element and the string when the former neared the latter before its re-excitation. Spectrogram (Figure 12) shows that it allowed replicating both ringing and damping--the harmonics became less distinct and pitch glides appeared. Moreover, such model predicted the fact that, even after a full fundamental string period, the signal spectrum did not return to its previous state, and some changes remained (Figure 11). Further improvements to the model are possible [20; 21; 22; 23]. Neither of the models was able to predict the actual measured spectra accurately. However, compared with the first model, the second one, at least, predicted the fact that the spectrum actually changed after a full string period (case of 12 ms in Figure 11). One can also observe a weak similarity in a spectral dip around 400 Hz between M1 and S2 in the same plot. In the case of a 70-ms delay (bottom plot in Figure 11) both models predicted spectral changes, but the improved model was able to slightly better reflect some details, such as peaks in the low-frequency range, around 220 Hz, 310 Hz, or 710 Hz, and, again, the area around 400 Hz. For better spectral behaviour, the model would need to consider more than a string, as some phenomena are located in the soundboard [19; 24]. Furthermore, the results were very sensitive to even small changes in simulation parameters, such as spectrum movement velocity, plucking position, plucking element profile, or material parameters. In order to closely reproduce a particular instrument, careful measurements need to be considered to precisely estimate values of these parameters. This could be achieved using a robot and serialised measurements. However, even the current model can be adjusted to closer resemble the actual instrument using multi-dimensional optimisations, though such process might be inefficient and time consuming, and would make sense only if the model needed to replicate a particular acoustic guitar.