## 4 Conclusions  
Parametric arrays have multiple applications in targeted audio delivery. However, the self-demodulation of the highly directive ultrasonic carrier is a non-linear process that introduces distortion of the audio signal. Multiple techniques have been proposed based on amplitude modulation. We have experimentally evaluated six different amplitude modulation techniques in terms of a frequency response as well as harmonic and intermodulation distortion. We analyzed the harmonic distortion at different frequencies and decomposed by orders. Additionally, the distortion of different modulation indices is evaluated for all the modulations techniques.  
When selecting a modulation technique and modulation index there must be a balance between sound quality and audio level. A large modulation index will lead to louder audible sound but with more distortion. In general, we recommend MAM1 with a modulation index of 0.6. This configuration produces the lowest levels of harmonic and intermodulation distortion while only decreasing the audible signal by 2 dB. MAM1 technique makes a good use of the limited bandwidth of the transducers. We acknowledge that for transducers with wider band (e.g., electrostatic speakers), MAM2 could provide better results. In any case, the ultrasonic transducers that we evaluated are the most commonly used in this type of devices.  
We hope that this study promotes more experimental measurements with parametric arrays that analyze the distortion of the speakers. The measurement technique that we used to avoid the appearance of spurious signal is based on selecting a microphone with an adequate frequency  
Figure 7: Comparison of \(IMD_{T}\) values for each modulation (m = 1).  
response, so it can be employed by most researchers. As future work, it would be desirable to measure psychoacoustical parameters and user-subjective measurements.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/6/2070/s1](http://www.mdpi.com/2076-3417/10/6/2070/s1)]([http://www.mdpi.com/2076-3417/10/6/2070/s1](http://www.mdpi.com/2076-3417/10/6/2070/s1)), Table SI: Main characteristics of the evaluated microphones, Figure S1: Block diagrams of preprocessing amplitude modulation techniques, Figure S2: Spectrogram of the signals corresponding to each stage of the measurement procedure, Figure S3: Harmonics up to the 5 th order measured with the predistortion techniques (m = 1), Figure S4: Level of total harmonic distortion (LTHD) for the predistortion techniques at different modulation indices, and Figure S5: Intermodulation distortion (IMDT) for the predistortion techniques applied with different levels of modulation index (m).  
Conceptualization, R.S.M. and A.M.; methodology, R.S.M. and A.V.; software, R.S.M.; validation, R.S.M., P.T. and A.V.; data curation, P.T. and R.S.M.; writing--original draft preparation, R.S.M.; writing--review and editing, R.S.M. and A.M. All authors have read and agreed to the published version of the manuscript.  
This work has been funded by the Spanish Ministry of Economy and Competitiveness through the R+D+I research project with reference BIA2016-76957-C3-2-R, and by the Government of Navarre through the Technology Transfer project 0011-1365-2019-000086.  
The authors declare no conflict of interest.