A theoretical foundation is development for horizontal holographic surround sound systems based on the two-dimensional Fourier transform. It is shown how the theory leads to the recording and reproduction of sound fields using circular arrays of microphones and loudspeakers. DFT processing of circular microphone arrays produces the spherical harmonics of the sound field, and is a generalization of certain higher order multipole microphones. The performance of the array is shown to be improved by using directional microphone elements. The angular sinc panning functions arise naturally from the reproduction theory, and a mode-matching approach further verifies that they are optimum at low frequencies. General windowing is reviewed for the control of artifacts at high frequencies and the radial error is proposed as a useful parameter for designing windows. Sound intensity theory is examined for visualizing surround sound fields, and a complex instantaneous velocity is introduced, which is easy to generate and equivalent to previous definitions for the case of monochromatic sound fields. The reproduction performance of a five-loudspeaker surround system is examined, and its performance over wider reproduction areas is also considered.
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