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When one visualizes a sound field as a means of treating noise sources, a detailed variation of the sound field is not required. It is sufficient to see source locations and overall variation of the field. A complex envelope in space can provide adequate information that one wishes to get because an envelope shows a gross change in signal. In other words, to interpret overall variation of sound fields in terms of a complex envelope is attempted. To achieve this objective, spatial complex envelopes have been defined firstly, and then a spatial modulation method to obtain the envelope has been theoretically developed and verified.
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Park et al. (2009) studied this question.
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