## 2 Materials and Methods
### Measurement Procedure  
The frequency response of a loudspeaker describes the range of audible frequencies that it can reproduce. For conventional devices, it is usually measured in an anechoic chamber where the loudspeaker under test is excited by a sweep signal \(x(t)\). This sweep typically ranges from 20 Hz to 20 kHz. The signal emitted by the speaker was then recorded with a flat response microphone to obtain the signal \(y(t)\). By means of FFT techniques, the impulse response \(h(t)\) and its corresponding transfer function were obtained:  
\[h(t)=iff\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\  
Other techniques use a condenser microphone orthogonal to the incident wave where its ultrasonic sensitivity is lower [24]. Thereby, the amplitude of the recorded ultrasonic waves is reduced while preserving the sound level in the audible range. This effectively prevents the generation of spurious signals. Based on the previous principle, we explored the use of a microphone with reduced ultrasonic sensitivity but good audio performance. Two condenser (GRAS AC40 - GRO, G.R.A.S. Sound & Vibration, Holte, Denmark, Behringer ECM8000 - BHO, Behringer International GmbH, Willich, Germany) and three dynamic (Shure SM57 - SH7, Shure Inc. Niles, Illinois, USA, Behringer XM8500 - BHX and BCT MD1 - BCT, Behringer International GmbH, Willich, Germany) microphones were selected for the study. Detailed specification can be found in Supplementary Table SI. The frequency response of the microphones in the audible range was measured by emitting sweeps with a monitor (Neumann KH120A, Georg Neumann GmbH, Berlin, Germany) with flat response (\(\pm\)2 dB between 54 Hz and 20 kHz) and is shown in Figure 3a. The same procedure was repeated in the ultrasonic range using the parametric speaker as an emitter. The responses are shown in Figure 3b. The response of the GRO microphone (i.e., upper curve) can be used as an approximation of the normalized frequency response of the ultrasonic emitter measured at 2 m since this microphone had the flattest ultrasonic response. The response of the parametric speaker peaked at 40.9 kHz, with a \(-\)3 dB bandwidth of 1.5 kHz and a \(-\)6 dB bandwidth of 3.9 kHz. This reduced bandwidth is the cause of a spurious signal being typically smaller at high frequencies. The progressive reduction of the levels at the sidebands, which are used to emit the modulated audio, leads to a partial reduction of the non-linearity acquired by the microphones. The dynamic microphones (i.e., SH7, BHX and BCT) registered a carrier level reduction of 30 dB. This means that the recorded audio is less likely to be affected by distortion artifacts generated from the high levels of pressure. This effect is illustrated in Figure 4, which shows the frequency responses obtained with different microphones when the ultrasonic array is emitting with a conventional AM modulation (i.e., DSBAM, described in further sections). For the two condenser microphones, GRO and BHO, the spurious signal was affecting the recordings along most of the frequency range. This was not the case when using the dynamic microphones. Their experimental curves show good agreement with the theoretical curves of a parametric loudspeaker. These curves were proportional to \(f^{n}\), where \(f\) is the frequency and \(n\) is the ratio between diffraction length and absorption length [16]. Diffraction length is the area of the transmitter divided by the wavelength at the primary frequencies and absorption length is the inverse of the nominal absorption coefficient at the primary frequencies. \(n=2\) corresponds to  
Figure 3: Relative frequency response of the different microphones. (**a**) Response in the audible range with a calibrated monitor as an emitter. (**b**) Response in the ultrasonic range with the ultrasonic array used as the emitter. Response normalized at carrier level measured by a GRO microphone. the Westervelt solution [6] for a large ratio, \(n=1\) is a good approximation to the solution obtained by [PERSON] and [PERSON] [25] for a small ratio.