Abstract: This paper,considering the structure of human auditory organ having an approximate rotation-symmetric property around the axis through two ears,proves and derives formulas for sound-image localization in the reproduced sound field when the listener fixes his head,and swings his head along the horizontal-or vertical-plane.These formulas may be used to calculate the localization distortion of sound-image in any reproduced sound field and to lead many different three dimensional surrounding sound systems and panoramic sound systems that have the minimum number of independent signal requared but no localization distortion of sound image in reproduction.
At last,the cases of three dimensional surrounding sound systems with cube array and triangular pyramid array models by using these formulas are illustrated for example in this paper.