Sound separation by generalized inverse
M. Yanagida, Osamu Kakusho · The Journal of the Acoustical Society of America · 1978
A statistical method to separate the sound waves from several sources is presented. The method is based on the generalized inverse of matrices in the frequency domain. The time domain expression for receiving the sound waves from n point-sources with m microphones is formulated in the system of m linear equations with n unknowns under the condition that the field is linear and homogenious, and that the sound pressure is inversely proportional to the distance. The system of equations is converted into that of the frequency domain by Fourier transform. Then, the least square solution is calculated using the generalized inverse technique and is again converted into the required solution in the time domain by inverse Fourier transform. This method is quite perfect under the ideal condition, but it has some difficulties under practical situations. Some investigations on such difficulties are studied on computer simulation.