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Shaping acoustic radiation induced by vibrotactile rendering on a touch surface

Many electronic devices with touch-sensitive surfaces aim to provide vibrotactile feedback, along with visual or auditory feedback, to facilitate the interaction between the user and the interface. In parallel to these efforts, recent studies developed various vibration rendering techniques,
 enabling more complex vibration patterns to be generated on the touch surface. However, few have addressed sound radiation induced by vibrotactile rendering on a touch surface, which could significantly impact the haptic interaction's overall perception. This study presents a method to shape
 the acoustic radiation due to rendering high-fidelity vibrotactile feedback on a touch surface. The proposed method utilizes measured frequency response functions and a vibroacoustic representation of the touch surface to define the relationship between actuator driving signals, vibration
 responses on the touch surface, and radiated sound power. Proper actuator driving signals are derived from the optimization problem formulated using the relationship. The proposed method was demonstrated through vibration rendering experiments on a touch surface comprising an acrylic plate
 and voice coil actuators. The results showed that the proposed method could shape the acoustic radiation while rendering target vibration patterns at desired positions on the touch surface. This study's proposed method could allow haptic engineers to design vibrotactile feedback and sound
 radiation simultaneously for a more compelling haptic experience.