ABSTRACT

INTRODUCTION
1.
Audible sounds such as music and voice are usually emitted by electrodynamic loudspeakers. An electrodynamic loudspeaker can transmit audible sound to a wide area because of its wider directivity. However, the audible sound emitted by electrodynamic loudspeakers can be a noise for non-target listeners [1]. Recently, to solve this problem, a parametric array loudspeaker (PAL) has attracted attention. The PAL can realize sharper directivity by utilizing an ultrasound wave and transmit the audible sound to a particular area [2,3,4]. Therefore, the PAL is expected to be used for announcements in museums, stations and so on. The PAL emits an intense amplitude modulated (AM) wave which is designed by modulating an ultrasound wave (carrier wave) with the audible sound [5]. The emitted intense AM wave is demodulated into the audible sound due to the nonlinear interaction in the air [6]. In the conventional modulation method, the frequency of the carrier wave is set at the resonance frequency of the ultrasonic transducer to intensely emit the AM wave. However, it tends to cause thermal runaway of the ultrasonic transducer because high load is applied to the ultrasonic transducer. Moreover, the vibration of the ultrasonic transducer constantly maximized because the frequency of the carrier wave coincides with the resonance frequency of the ultrasonic transducers, and it induces thermal runaway of the ultrasonic transducer. As a result, spectral peak noises are generated from a PAL including the ultrasonic transducer in which thermal runaway has occurred (crashed PAL). Especially, this is a severe problem in intensely emitting carrier wave using the audio-spot design based on separating emission with the carrier and sideband waves [7]. This is because it is necessary to emit intensely the carrier wave from the PAL compared with the conventional PAL, and the spectral peak noises are remarkably generated. Here, we focus on the fact that the power of the spectral peak noises depends on the frequency of the carrier wave and the carrier wave of the pure tone induces thermal runaway of ultrasonic transducers. We have proposed the thermal runaway control method with the frequency modulated carrier wave for the PAL [8]. The proposed method designs the AM wave with the frequency modulated carrier wave that the frequency of the carrier wave changes with time. As the frequency of the carrier wave changes with time, the power of the spectral peak noises also changes. Consequently, the power of the spectral peak noises can be reduced. Experiment results show that the proposed method can achieve load reduction to the ultrasonic transducer.
2. PALAMETRIC ARRAY LOUDSPEAKER
2.1
Principle of Parametric Array Loudspeaker
The PAL can realize sharper directivity by utilizing the ultrasound wave. It emits the AM wave which is designed by modulating the amplitude of the ultrasound wave (carrier wave) with the audible sound. Audible sound source demodulates from the intense AM wave emitted from the PAL by the non-linear interaction in the process of propagation in the air. The carrier wave c(t) and the audible sound s(t) are indicated as follows:
where t  is a time index, Ac  and As  are the maximum amplitudes of the carrier wave and the audible sound, fc  and fs  are the frequencies of the carrier wave and the audible sound. The AM wave  vAM(t) is designed by modulating the carrier wave with the audible sound. From Eq. (1) and (2), the AM wave  VAM(t) is indicated as follows:
where  a  (0 < a ≤ 1)  is an amplitude modulation index. Equation (3) can be transformed as follows by trigonometric functions. VAM(t) = {1 + as(t)}c(t)
From Eq. (5), it can be confirmed that the AM wave consists of the carrier wave (frequency:  fc), the lower sideband wave (frequency: fc - fs) and the higher sideband wave (frequency: fc + fs) [9]. The original audible sound demodulates as the difference tone between the carrier wave and sideband waves. The demodulated sound s'(t) are indicated as follows: (6) s'(t) = DM[vam(t)] ≈ s(t), where DM[.] is expressed demodulation. The demodulated audible sound has a sharper directivity as with the ultrasound wave. Therefore, the PAL can transmit the original audible sound to a particular area.
2.2
Problem of Parametric array loudspeaker
The ultrasonic transducer of the PAL has a frequency response with steep peak at the resonance frequency. In the conventional modulation method, the frequency of the carrier wave is set at the resonance frequency of the ultrasonic transducer to intensely emit the AM wave. However, it tends to cause thermal runaway of ultrasonic transducers because high load is applied to the ultrasonic transducer for the extended period of time. As a result, the spectral peak noises are generated from the Figure 1 – Spectrograms of the observed carrier wave. crashed PAL. Figure 1 shows the spectrograms of the observed carrier wave of  40  kHz from a normal PAL and the crashed PAL. In Fig. 1, a horizontal axis shows time, a vertical axis shows frequency and a color bar represents the power of the frequency. From Fig. 1(b), we can confirm that the several spectral peaks of the noises appeared  4~20  kHz as compared with Fig. 1(a). In addition, the vibration of the ultrasonic transducer is constantly maximized because the frequency of the carrier wave coincides with the resonance frequency of the ultrasonic transducer. Thus the power of the spectral peak noises becomes maximum at this time. As indicated by the following equation, the spectral peak of the noises tends to appear around the frequency of the specified fraction of the integral number of the frequency of the carrier wave.
where Z is a set of whole integral numbers. Therefore, we have proposed the thermal runaway control method of the crashed PAL.
THERMAL RUNAWAY CONTROL METHOD WITH FREQUENCY MODULATED
3.
CARRIER WAVE IN PARAMETRIC ARRAY LOUDSPEAKER
Modulation Method Using Frequency Modulated Carrier Wave
3.1
We have proposed the thermal runaway control method of the crashed PAL. In the proposed method, we design the AM wave with the frequency modulated carrier wave which has been designed in such a way that the frequency of the carrier wave changes with time. Figure 2 shows the overview of the proposed method. In Fig. 2, c ( t ) shows the carrier wave, and c ρ ( t ) shows the frequency modulated carrier wave. In the 1st step, this method modulates the frequency of the carrier wave with modulation signal to design the frequency modulated carrier wave. The frequency modulated carrier wave Cp(t) and the modulation signal m(t) are indicated as follows:
where AM  is the maximum amplitude of the modulation signal, fM  is the frequency of the modulation signal, Af is the frequency deviation, kFM is the deviation constant, and FM[j] is a function that conducts frequency modulation [10]. Equation (8) can be transformed as follows by trigonometric functions.
In the 2nd step, this method modulates the amplitude of the frequency modulated carrier wave with the audible sound to design the AM wave. The AM wave  vp(t) is indicated as follows:
In the proposed method, we design the AM wave with the frequency modulated carrier wave that the frequency of the carrier wave changes with time. Therefore, the frequencies of sideband waves also change with time. Accordingly, the difference tone between the carrier and the sideband waves, namely the demodulated sound, is demodulated in the same way as in the case for the conventional modulation method. The demodulated sound s'p(t) are indicated as follows:

3.2
Constraint Conditions of Modulation Parameters
As mentioned in the previous section, the ultrasonic transducer has the frequency response with steep peak at the resonance frequency. Therefore, the larger the difference between the frequency of the carrier wave and the resonance frequency of the ultrasonic transducer, the power of the demodulated sound is reduced. As a result, the power of the demodulated sound depends on both of the frequency deviation Af and the frequency of the modulation signal fM. The frequency deviation means the maximum amount of the frequency change against the frequency of the carrier wave. The frequency of the modulation signal indicates the change period of the frequency of the carrier wave. The smaller the difference between the frequency of the carrier wave and the resonance frequency of the ultrasonic transducer, the power of the spectral peak noises and that of the demodulated sound become larger. Thus, the larger the frequency deviation, the difference between the frequency of the carrier wave and the resonance frequency of the ultrasonic transducer becomes larger. Consequently, the power of the demodulated sound is reduced. In addition, the larger the frequency of the modulation signal, the shorter the modulation period for the frequency of the carrier wave. Consequently, the fluctuation period of the power of demodulated sound is shortened. As a result, the power of the demodulated sound becomes unsteady. In conclusion, the power of the demodulated sound needs to be maintained at the comparable level used the conventional modulation method. Therefore, the appropriate frequency deviation and the frequency of the modulation signal need to be established to reduce the spectral peak noises. Figure 3 shows the frequency response of the PAL without modulation. In Fig. 3, a horizontal axis shows frequency, a vertical axis shows the power of the frequency. We thought that if the power reduction of the frequency of the carrier wave is less than 6 dB, it is no problem for human auditory characteristics. Thus, the frequency of the modulation signal fM is defined as the following equation. (14) Δf < Δfmax› Afmax is the maximum amount of the frequency deviation. From Fig. 3, the maximum where Afmax is set to 1000 Hz. In addition, it is known that a amount of the frequency deviation demodulated sound is generated by frequency modulation in the PAL. Thus, it is necessary to set the frequency of the modulation signal fM so that the demodulated sound generated by frequency modulation does not become a noise. Thus, the frequency of the modulation signal fM is defined as the following equation. (15) fm < fMmax' where fMmax is the maximum value of the frequency of the modulation signal. Figure 4 shows the frequency response of the demodulated sound. From Fig. 4, the PAL is difficult to represent the sound in lower-frequency band. Therefore, we set the frequency of the modulation signal fM as the lower-frequency band that sound pressure is 20 dB lower than that of 4 kHz. From Fig. 4, the maximum value of the frequency of the modulation signal fmmax is set to 500 Hz.
4. EVATUATION EXPERIMENT
Evaluation Experiment for Spectral Peak Noise Reduction
4.1
We carried out the evaluation experiment to confirm the effectiveness of the proposed method. We measured the power of the spectral peak noises generated from the crashed PAL in the conventional and the proposed methods. Specifically, we measured the time transition of the power of the spectral peak noises when emitting the frequency modulated carrier wave for 20 minutes. In this experiment, the frequency of the carrier wave is set at the resonance frequency of the PAL calculated using time stretched pulse (TSP) method [11], and three crashed PALs are used in consideration of individual differences. Also, modulation parameters were determined from the preliminary experiment. Table 1 shows the experimental equipment, and Table 2 shows the experimental conditions.

4.2
Experimental Result for Spectral Peak Noise Reduction
Figure 5 shows the experimental result for spectral peak noise reduction, and Table 3 shows the power of the spectral peak noises. In Fig. 5, a horizontal axis shows each carrier wave, a vertical
axis shows the power of the spectral peak noises. Figure 5 is normalized the power of the spectral peak noise in the conventional method to 20.0 dB. From Fig. 5 and Table 3, we confirmed that the spectral peak noise reduction performance had individual differences. In addition, we confirmed that the spectral peak noises were reduced by an average of 4.8 dB for crashed PAL(A), and 10.5 dB for crashed PAL(B). However, in crashed PAL(C), we confirmed that the spectral peak noise increased by 5.5 dB on average. The reason is considered to be that the optimum modulation parameters differ depending on the individual. Moreover, the spectral peak noise reduction performance changes with time. Thus, the optimal modulation parameters are expected to change with time. From the experimental result, we confirmed that the proposed method can reduce the spectral peak noises for the crashed PAL.
CONCLUSIONS
5.
The PAL has a sharper directivity and can transmit an audible sound to only a particular area by utilizing the ultrasound wave. However, it tends to cause thermal runaway of the ultrasonic transducer because high load is applied to the ultrasonic transducer when the AM wave of the conventional modulation method is emitted for the extended period of time. In addition, spectral peak noises are generated from the crashed PAL. Therefore, we have proposed the thermal runaway control method with the frequency modulated carrier wave for the PAL. In this paper, we further evaluated the spectral peak noise reduction performance of the proposed method. Concretely, we measured the time transition of the power of the spectral peak noises when emitting the frequency modulated carrier wave for 20 minutes. From the result of the evaluation experiment, we confirm the effectiveness of the proposed method. In the future work, we intend to change modulation parameters adaptively to control thermal runaway of the crashed PAL.
ACKNOWLEDGEMENTS
This work was partly supported by JST COI, and JSPS KAKENHI Grant Number JP18K19829, JP18K11365 and JP19H04142.