Randomness and the reverberation time, RT60, of acoustic responses

This paper investigates an implication of the clustering, on the complex plane, of the roots of transfer function polynomials obtained from acoustic responses. These polynomials can be the high order transfer functions obtained from room impulse responses or the relatively lower order ones obtained from head related impulse responses. This clustering behavior is explained using results from the theory of the roots of random polynomials. It is demonstrated that, although they do not appear that way, the coefficients of acoustic polynomials can be modeled as random polynomials with certain constraints applied. In the case of room impulse responses, the median of their clustered roots is shown to be directly related to the reverberation time of the room. This is shown to be an accurate measure of the reverberation time by comparison with other estimation techniques.