Expanded acoustic reciprocity and directivity synthesis of musical instruments using microphone array

The well-known acoustic reciprocity ensures the invariance of the transfer function when swapping the positions of the sound source and the receiver. This research expands acoustic reciprocity, ensuring the invariance of the transfer function when swapping the directivity of the sound source and the receiver. The proof of this principle is based on a novel model of directional receivers, and its description is concise. Furthermore, as an application example of this principle, we propose the directivity synthesis of musical instruments using a microphone array. We can compose arrays with a large number of transducers because normally receivers are smaller than speakers. Therefore, directivity synthesis for more complex scenarios can be achieved. In this sense, this measurement method has the advantage compared to the conventional method using speaker arrays.