In recent years, applications such as virtual reality (VR) systems and room acoustics simulations have brought the modeling of sound source directivity into focus. An accurate simulation of directional responses of sound sources is essential in immersive audio applications.
Real sound sources have directional properties that are different from simple sources such as monopoles, which are sources frequently used for modeling more complex acoustic fields. For instance, the sound level of human speech as a sound source varies considerably depending on where the sound is recorded with respect to the talker’s head. The same is true for loudspeakers, which are considered linear and time-independent sources. When the sound is recorded behind the speaker, it is normal to observe differences of up to 20 dB SPL at some frequencies. The directional characteristics of sound sources become particularly pronounced at high frequencies. The propagation of real sound sources, such as human voices or musical instruments, differs from simple source models like monopoles, dipoles, and quadrupoles due to their physical structures.
The common approach to measuring directivity patterns of sound sources involves surrounding a sound source in an anechoic chamber with a high number of pressure microphones on a spherical grid and registering the sound power at these positions. Apart from the prohibitive hardware requirements, such measurement setups are mostly impractical and costly. Audio system manufacturers have developed various methods for measuring sound source directionality over the years. These methods are generally of high technical complexity.
This article proposes a new, reduced-complexity directivity measurement approach based on the spherical harmonic decomposition of the sound field. The method estimates the directional characteristics of sound sources using fewer measurement points with spherical microphone arrays. The spherical harmonic transform allows for the calculation of directivity using data collected from spherical microphone arrays instead of pressure sensors. The proposed method uses both the pressure component and spatial derivatives of the sound field and successfully determines directivity with sparse measurements.
An estimation model based on the spherical Fourier transform was developed, measurements were carried out to test this model, and preliminary results obtained from the estimation model are presented. Experiments conducted at the METU Spatial Audio Research Laboratory demonstrated the effectiveness of the proposed method. The directivity characteristics of Genelec 6010A loudspeaker are measured using eight 3rd-order spherical microphone arrays. The directivity functions obtained were highly consistent with the data provided by the loudspeaker manufacturer. The results, especially in low and mid-frequency bands, indicate the utility of the proposed method.
