An algorithm for generating reverberation as an application of the chaos technique—Return map derived from initial responses

Abstract

To synthesize the acoustics of a large enclosure with the aid of a computer, an algorithm for adding reverberation to the initial response is proposed. When the initial response is known, the arrival time and the intensity for each subsequent reflective sound are calculated one after another. After calculating the time intervals between each succeeding initial reflective sound and processing them to form a suitable random-number generator, each future arrival time is then successively determined. From this generator, a return map, often used in the chaos technique, is adopted. As for the intensity, with the input value of reverberation time (RT60) the decay rate is determined; from this, the decay rate and the cumulative intensity of the initial reflective-sound decay curve as a standard are estimated. Then each future intensity is determined by comparing the cumulative values to the standard. No awkwardness was heard from the burst tone convoluted with such a calculated response. Dimensional analysis about the time intervals in the long-time response calculated by the same algorithm as that used for initial response did not show that they were from random processes.