Abstract
Transfer funcion in a room is approximated to a stationary Gaussian process, if the direct transmission of sound from the source to a receiving point is negligible. The impulse response in a room, therefore, is considered as a Gaussian process, since it corresponds to the inverse Fourier transform of the transfer function. Gassian process, in general, can be described by an auto-correlation function and a mean value of the process, and hence the auto-correlation function of the impulse response gives an expression of the statistic property of the sound field in a room considering the fact that the mean value of the process is zero. Since the auto-correlation function has a relation of the univalent correspondence with the ensemble average of the short-time power spectrum of the impulse response(Eq. 10), eventually the ensemble average of the short-time power spectrum is available the description of the statistic property of sound field in a room. It has an advantage in that it is characterized by the decaying aspects of sound and their dependence on frequency. The ensemble average of short-time power spectrum, therefore, is very useful for the investigation of acoustical property of room. The ensemble average of the short-time power spectrum can be deduced from the space and time averages of the short-time power spectrum of the impulse response in a room(Eq. 11)and the accuracy of the estimation may be represented by means of the normalized variance of the averages(Eq. 14). The relationship between the normalized variance of the averages of the short-time power spectrum of the impulse response and the average frequency band width of its short-time power spectrum can be expressed by the integral of its auto-correlation function(Eq. 18). The resultant formula is approximated to the following:σ_r^2=(1+2l/λ)^<-1>(1+WeqT_R')^<-1>(47)where l is the average length, λ is the wave length, Weq is the frequency band width of the short-time power spectrum(Eq. 39)and T_R' is the equivalent duration of time average(Eq. 46). Experimental results show a good agreement with the theoretical ones(Figs. 1, 2, 3, 4, 5).
