Sound field reproduction based on least-squares method

Abstract

Sound field reproduction is one of the representative three dimensional sound technologies. Most of sound field reproduction techniques cannot reproduce the sound field at arbitrary specified control volume independently of control source array. To reproduce the sound field at specified control volume, Least-Squares Method (LSM) was studied. The goal of this method is to reproduces target sound field induced by virtual source using loudspeaker arrays by minimizing sound field error in least-squares sense. With this objective, new cost function for sound field reproduction is defined as integration in time and space domain of square difference between sound pressures in control area occurred by virtual point source and reproduced by speaker system. The optimal filter is decided to minimize this cost function. But in this case unpractical solution can be obtained. To avoid that, we applied some constraints about input energy in this research. To verify the suggested method, the comparison with Wave Field Synthesis method (WFS) was preformed through numerical simulation. As a result, LSM solution makes smaller error between target field and reproduced field than that of WFS.