Virtual Bass Enhancement Based on Harmonics Control Using Missing Fundamental in Parametric Array Loudspeaker GENG, Yuting1 Ritsumeikan University 1-1-1 Nojihigashi, Kusatsu, Shiga, Japan NAKAYAMA, Masato2 Osaka Sangyo University / Ritsumeikan University 3-1-1 Nakagaito, Daito, Osaka, Japan / 1-1-1 Nojihigashi, Kusatsu, Shiga, Japan NISHIURA, Takanobu3 Ritsumeikan University 1-1-1 Nojihigashi, Kusatsu, Shiga, Japan ABSTRACT Parametric array loudspeaker (PAL) can achieve a sharp directivity by using an ultrasonic wave. However, PAL has difficulty emphasizing bass sounds compared with conventional dynamic loudspeakers because it utilizes demodulation based on nonlinear interaction in the air. Also, the sound with PAL is degraded by harmonic distortion with intermodulation. Here, we focus on the missing fundamental, a psychoacoustical phenomenon indicating that human beings perceive a pitch of fundamental by harmonics. Based on this phenomenon, virtual bass enhancement has been proposed for small dynamic loudspeakers and applied on PAL. However, those harmonic generators are not suitable enough for PAL because PAL generates much more harmonic distortion than dynamic speakers. Therefore, in this paper, we propose virtual bass enhancement on basis of harmonics control adapted to harmonic distortion of PAL. The proposed method uses missing fundamental and employs a pre-processing to reproduce the virtual bass sound by stressing harmonics of acoustic signals. It re-allocates energy to higher harmonics to amplify the demodulated sound with high-shelf filter. In addition, the proposed method controls the harmonics to cause the missing fundamental and reduce the distortion of the demodulated sound using peak filters. Finally, we confirmed the effectiveness of the proposed method through evaluation experiments. Keywords: Harmonics control, Virtual bass enhancement, Parametric array loudspeaker I-INCE Classification of Subject Number: 00 _______________________________ 1 [email protected] 2 [email protected] 3 [email protected] 1. INTRODUCTION Audible sounds such as music and voice are usually reproduced by conventional dynamic loudspeakers. However, widely carried sounds become noise for non-listeners. In recent years, parametric array loudspeaker (PAL)1,2 has received attention for its sharp directivity. PAL emits an intense amplitude modulated (AM) wave synthesized by modulating the ultrasonic wave with audible sound. The emitted intense AM wave is demodulated from ultrasonic wave to audible sound by nonlinear interaction in the air, and the demodulated audible wave achieves sharp directivity. Therefore, PAL can reproduce audible sound in a particular area3, and is promising to be used in museums, stations and so on. However, there are two major limitations of the PAL which lead to a lower reproduction performance than conventional dynamic loudspeakers2. First, due to the physical principle of demodulation, it is difficult for PAL to reproduce bass sounds. Second, the sound quality is degraded by harmonic distortion and intermodulation. Since the poor bass reproduction of PAL is physically unsolvable1, in order to reproduce the low-frequency sounds with a satisfying sound pressure, the total output energy should be increased significantly. As an alternative solution, a psychoacoustic approach is carried out. Based on missing fundamental4, the virtual bass enhancement generating harmonic series to let listeners perceive bass sounds is carried out for small-scale loudspeakers5, and this study is also applied to the PAL6. Since PAL generates much more harmonic distortion over dynamic loudspeakers, the nonlinearity of PAL is considered. The conventional method adapted the harmonic generator for small-scale loudspeakers to the PAL and designed an equivalent harmonic generator to obtain the same harmonic components. The conventional method resulted in an improvement of bass sounds with a cost of severe sound quality losses. However, the conventional method is less effective for harmonic sounds (sounds with harmonic structure, e.g. voice, string instruments and so on) than inharmonic sounds (sounds without harmonic structure, e.g. drums and so on) and resulted in a smaller sound pressure improvement and bigger loss of sound quality. Therefore, we focus on the difficulty of PAL in low-frequency reproduction and the harmonic distortion generated in demodulation. We suppress low-frequency components for an increasement of energy conversion efficiency. Missing fundamental is utilized for fundamental perception with harmonic series, so the energy of low- frequency components can be allocated to other components for an increasement of energy conversion efficiency. Double sideband (DSB) modulation can achieve a higher sound pressure over other modulation method but generates more harmonic distortions. We make use of these harmonic distortions, which are regarded as useless by-products in past studies. First, frequencies of harmonic distortions are multiples of fundamental, so they contribute to create missing fundamental effect. Moreover, harmonic distortions generated by low-frequency components have a same frequency as high-frequency components in audible sound, so we can utilize harmonic distortions to enhance high- frequency components. In this paper, we propose a virtual bass enhancement based on harmonics control for harmonic sounds with low fundamental frequency. We utilize high shelving filter (HSF) to suppress the low-frequency components, allocate energy to high-frequency components, and improve the sound pressure of demodulated sound. Missing fundamental is created in a higher sound pressure as a compensation of sound quality to suppression of low-frequency components. Then, we utilize a sequence of peaking filters (PKF) to control the proportion of harmonic components under a designed strategy using the inverse frequency response of PAL. Due to the harmonics control, the loss of sound quality can be reduced, and an improvement of sound quality is possible to achieve. Audible band Ultrasonic band Power Target audible sound f Frequency Second-order S harmonic distortion Audible sound: s(t) Amplitude Power Power Demodulation modulation Power Frequency Frequency f -f fC-fS fC fC+fS fS 2fS C S fC fC+fS Modulated wave: u (t) Demodulated wave f Frequency AM C (Ultrasonic wave) Carrier wave: c(t) (Ultrasonic wave) Figure 1 Overview of modulation and demodulation of parametric array loudspeaker 2. PARAMETRIC ARRAY LOUDSPEAKER 2.1 Principle of Parametric Array Loudspeaker PAL can realize a sharper directivity by utilizing a parametric array effect1 in the air. Figure 1 shows the overview of modulation and demodulation of PAL. PAL emits an intense amplitude modulated (AM) wave which is synthesized by modulating an ultrasonic carrier wave with audible sound. The carrier wave �(�) and audible sound �(�) can be indicated as follows: �(�) = �( cos(2��(�), (1) �(�) = �0 cos(2��0�), (2) where � denotes time index, �( and �0 denote the amplitudes of carrier wave and audible sound, �( and �0 denote the frequencies of carrier wave and audible sound respectively. The emitted AM wave �23(�) can be indicated as follows: �23(�) = {1 + ��(�)}�(�), (3) where � = �0/�( (0 < � ≤ 1) denotes the modulation factor. Equation (3) can be transformed as follows with Eqs. (1) and (2): 1 � (�) = � cos(2�� �) + � >{cos(2�(� + � )�) + cos(2�(� − � )�)}. (4) 23 ( ( 2 0 ( 0 ( 0 From Eq. (4), the AM wave consists of carrier (frequency: �( ), upper sideband (frequency: �( + �0 ), and lower sideband (frequency: �( − �0). The emitted AM wave is self-demodulated into audible sound by nonlinear interaction in the air. The demodulated audible sound is the difference in frequency domain between carrier wave and upper sideband, or between carrier wave and lower sideband. Since the target sound is a result of interaction between two ultrasonic waves, it derives the sharp directivity of ultrasonic waves. Thus, PAL can carry audible sound to particular area. 2.2 Problems of Parametric Array Loudspeaker There are two major problems with the PAL. One is loss of sound quality due to harmonic distortion, and the other one is low sound pressure in low-frequency band. First, PAL suffers from harmonic distortions much more than conventional dynamic loudspeakers since it utilizes the nonlinear interaction in the air. As shown in Fig. 1, in case of utilizing the DSB modulation, the original audible wave is demodulated as the difference between carrier wave and each sideband. However, the second harmonic distortion is demodulated between two sidebands. Intermodulation will also occur much more if the original audible sound has several frequency components. The harmonic distortions and intermodulation cause the sound quality degradation of PAL. In addition, Figure 2 Missing fundamental effect PAL has theoretical difficulties in reproducing bass sounds1. The nonlinearity of the PAL can be described with the sound pressure of demodulated sound as follows: � �> � ∝ C |�(�′)|, (5) � ��F> where � denotes the sound pressure of demodulated wave at observation point on the direction of propagation, �C denotes the source sound pressure, � denotes the distance F between PAL and observation point, � = � − �/�C is the retarded time with speed of sound �C, �(�′) is the envelope of AM wave. In the case when �(�) is a sinusoidal wave as indicated in Eq. (2), Eq. (5) can be altered as � � ∝ C ∙ 4�>�>�� cos(2�� �F). (6) � 0 0 0 Equation (6) suggests that the sound pressure of