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Pressure matching (PM) method is an effective method to control a sound field using many loudspeakers. It is difficult to implement PM method because it requires multi-point room impulse response (RIR) measurements. Multi-point measurements are challenging because they require a large number of microphones and a narrow sampling interval when dealing with high frequencies. Therefore, to synthesize a sound field in a local region, we proposed a PM method using estimated RIRs from only a small number of measurements based on the sparse Equivalent Source Method (ESM). In the previous method, we modeled the transfer functions considering only the direct sound from the loudspeaker. However, when the sound field is synthesized in the actual environment, the reflected sounds must be considered. In this study, we propose a PM method using the estimated transfer functions by sparse ESM based on the image source method considering the direct sound and early reflected sounds. In the experiment, we evaluated the accuracies of synthesized sound field by the proposed method compared to the methods only considering the direct sound.

In the field of room acoustics, it is important to find the absorption coefficients of the wall surface, which is a boundary condition for modeling the room acoustic field. However, it is not easy to measure the acoustic impedances of the entire room because it requires many measurement points near the wall surface. Recently, a method to estimate the acoustic impedance and absorption coefficients by using both measurement and simulation methods has been proposed. However, a large number of measurement points are required to obtain sufficient estimation accuracy. In this study, we proposed estimation method of the sound absorption coefficients using machine learning with virtually increasing the number of microphones. First, the transfer functions at the virtual microphones are obtained from small number of transfer functions based on the sound field modeling by sparse equivalent sources. Then, the both transfer functions at the virtual and real microphones are used as the training data for machine learning. To evaluate estimation accuracy of the proposed method, we conducted the two-dimensional simulation experiments based on the boundary element method.

The Room Impulse Response (RIR), which indicates the propagation characteristics of sound, is used in various acoustical applications. In particular, multi-point measurement of RIRs is important for applications that require spatial information, and measurement of these is difficult. Previously, spatial interpolation methods of RIRs based on physical models have been proposed. Especially, the sparse Equivalent Source Method (ESM) with Image Source Method (ISM) acheive the spatial interpolation of the early reflected sounds with higher accuracy at high frequency. However, this method has a problem that when the order of reflected sounds to be estimated increases, it becomes difficult to find the optimal solutions because the number of bases increases. In this study, to reduce the number of bases in each optimization problem, we proposed a sparse ESM with the image sources grouped by the arrival times of reflected sounds. The optimization problem for each group of image sources is individually solved. In the simulation experiment, it is revealed that the proposed method can estimate higher-order reflections with higher accuracy compared to the conventional method. In addition, we found that the estimated region with high accuracy became broader.

Measurements of Room Impulse Responses (RIRs) at multiple points have been used in various acoustic techniques using the room acoustic characteristics. To obtain multi-point RIRs more efficiently, spatial interpolation of RIRs using plane wave decomposition method (PWDM) and equivalent source method (ESM) has been proposed. Recently, the estimation of RIRs from a small number of microphones using spatial and temporal sparsity has been studied. In this study, by using the measured RIRs, we compare the estimation accuracies of RIRs interpolation methods with a small number of fixed microphones. In particular, we consider the early and late reflections separately. The direct sound and early reflection components are represented using sparse ESM, and the late reflection component is represented using ESM or PWDM. And then, we solve the two types of optimization problems: individual optimization problems for early and late reflections decomposed by the arrival time and a single optimization problem for direct sound and all reflections. In the evaluation experiment, we measured the multiple RIRs by moving the linear microphone array and compare the measured and estimated RIRs.

The visualization of the sound field which is an invisible-physical phenomena is useful for detection of noise sources, understanding the sound propagation, and architectural acoustics. Room Impulse Response (RIR) is widely used in various acoustic applications because RIR characterizes the sound propagation between a source and a measurement point in a room. Thus, measuring the RIRs at multiple points allows us to visualize the sound field in more detail. For example, we can observe the animation of sound wave fronts by using the RIRs at multiple points. However, many microphones and repetitive measurements are required to measure the RIRs with high resolution. In this paper, we propose a method for visualization of the sound field with high spatial resolution based on the estimation of the RIRs around the microphone using a small number of microphones. The RIRs are modeled using sparse equivalent sources and the image source methods. We conducted the evaluation experiment in an anechoic chamber. By animating the RIRs estimated by three microphones, the sound wave fronts including direct sound and primary-reflection can be clearly observed.

The spatial transfer function (STF) is important for many acoustic technologies. However, it is not easy to measure STFs at multiple points. We propose a method of estimating the sound field using a small number of microphones to make it easier to measure STFs. By using equivalent sources, STFs are modeled to extrapolate the sound field including primary reflections. We investigated the effect of the arrangement of the microphone array configuration and the robustness to noise for the proposed method. It was found by simulation that the proposed method provided better estimation accuracy, especially extrapolation, than linear interpolation.

Auditory display techniques require subjective evaluations of the virtual sound field to determine the accuracy of a reproduced sound with respect to a listener’s perception of spatial information. To synthesize a physically accurate sound field, local sound field synthesis limits the controlled area inside the loudspeaker array. The size and position of the controlled area affects the accuracy of the synthesis. In this study, we investigate the sound localization accuracies at different positions inside a 2Dimensional loudspeaker array by measurement of the interaural level differences in an anechoic chamber. The results show that the sound localization of the local sound field synthesis was more accurate than the conventional wave field synthesis, if a suitable parametrization of local listening area is chosen.

Many physical sound field synthesis techniques have been studied. To implement these techniques, a large-scale reproduction system is usually required with a large number of loudspeakers, D/A converters, and amplifiers. Thus, the techniques are not suitable for use in a rooms of an ordinary house. In our recent studies, a physical sound field reproduction system was developed with a digital loudspeaker array and suitable for an ordinary, small room. To more accurately reproduce the sound field with the implemented loudspeakers, an effective method is local sound field synthesis (LSFS). Because the area of the reproduced sound field is limited in LSFS, the reproduction area must track the listener's head movement. To track the listener's head movement, the driving functions of loudspeakers must be changed in real time. In this study, the effect of switching the reproduction area is investigated to determine the appropriate switching rate and size of the local area.

The room impulse response (RIR) is important in most acoustic applications, such as the design of concert halls and sound field control, because it characterizes the sound propagation. The measurement of RIRs at multiple points is challenging, as it requires a huge microphone array or repeating the experiment by microphone replacement. Several RIR interpolation and extrapolation methods of RIRs have been developed for obtaining RIRs from multiple measurement points efficiently. Extrapolation methods offer more efficient RIR measurement compared to interpolation. However, previous studies focused on extrapolation at frequencies below 1 kHz, and the extrapolation at higher frequencies was difficult. In this study, we propose an extrapolation method for RIRs of direct sound and early reflections in a local area using a small number of measurement points. The proposed method represents the RIRs around the microphones using superpositions of sparse equivalent sources located around the loudspeaker and image sources. We conducted a measurement experiment in an anechoic chamber to estimate RIRs around microphones using sound-reflecting boards. From the experimental results with 2.5 dimensional conditions, the proposed method achieved about above 10 dB of signal to noise ratio (SNR) near the microphone array from 0.5–8.5 kHz. For the extrapolation accuracy over the entire evaluation area (0.6 × 0.54 m2), the proposed method improved the SNR by about 5–6 dB compared to results using the plane wave decomposition.