impression of a sound source inside of the inner room by comparison the calculation of delay times and attenuation factors in relation to the center of the room in accordance with embodiments of the present invention not only solves the above problem but also seamlessly accounts for the delay time simulation of imaginary speakers at the perimeter of an imaginary room by the physical speakers located at the perimeter of the primary inner room due to the fact that in this improved model attenuation factors are calculated in relation to the distance between the source and the center of the room when a source is at the center of the room all speakers are engaged with the least amount of attenuation thus the resulting impression could perceptually become much stronger compared to when the source is at a considerable distance from the center even though u03b3 in equation 9 could be used to control the relation between attenuation of sounds due to distance the addition of u03bb as a constant has been found to be useful to balance the sound levels between the simulated impressions when the source is in the center of the room or when it is her away assuming that the improved model described above is utilized.