Center for Noise and Vibration Control, Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea.
J Acoust Soc Am. 2013 Sep;134(3):2106-17. doi: 10.1121/1.4817876.
For the derivation of 2.5-dimensional operator in wave field synthesis, a virtual source is assumed to be positioned far from a loudspeaker array. However, such far-field approximation inevitably results in a reproduction error when the virtual source is placed adjacent to an array. In this paper, a method is proposed to generate a virtual source close to and behind a continuous line array of loudspeakers. A driving function is derived by reducing a surface integral (Rayleigh integral) to a line integral based on the near-field assumption. The solution is then combined with the far-field formula of wave field synthesis by introducing a weighting function that can adjust the near- and far-field contribution of each driving function. This enables production of a virtual source anywhere in relation to the array. Simulations show the proposed method can reduce the reproduction error to below -18 dB, regardless of the virtual source position.
为了从波动场综合中推导出 2.5 维算子，假设一个虚拟声源被放置在远离扬声器阵列的位置。然而，当虚拟声源放置在阵列附近时，这种远场近似不可避免地会导致再现误差。在本文中，提出了一种在连续线阵列扬声器附近和后面生成虚拟声源的方法。通过基于近场假设将面积分（瑞利积分）简化为线积分，推导出一个激励函数。然后，通过引入一个权函数，将该解与波动场综合的远场公式相结合，该权函数可以调整每个激励函数的近场和远场贡献。这样，就可以在与阵列有关的任何位置产生虚拟声源。模拟结果表明，无论虚拟声源的位置如何，该方法都可以将再现误差降低到-18dB 以下。
