Phase response of transfer functions and coherent field in a reverberation room

Abstract

SUMMARYThis paper analyzes the properties of sound field transfer functions that change with the sound source distance (SSD), by measuring reverberant room impulse responses from a point of view of the phase characteristics. We analyzed the propagation phase (PP) according to the SSD in a reverberant field that R. Lyon investigated, by using a narrow-band linear regression analysis of the impulse responses and considered the relation to the zero distribution of the transfer function. As a result, we clarified that the SSD information is included in the phase frequency characteristics of the minimum-phase component and the variances from the PP. The distance from the source where the PP could be observed corresponds to the coherent field based on the wave theory or the critical distance defined by the energy ratio of direct to reverberation sound. Therefore, the field where the PP could be observed in the minimumphase component of the transfer function can be treated as the direct sound field. In addition, we also present that the reverberation phase (RP) separated and extracted along with PP from the phase frequency characteristics is according to the estimated value from the number of non-minimum-phase zeros.

Room Transfer Function

“…We call this the propagation phase [10]. We can find the trend for the propagation phase even in a three-dimensional system like reverberant space [17]. Figure 10 shows the measured impulse responses.…”

“…Because the minimum-phase characteristics are such that the accumulation phase becomes 0 as shown in the figure, we were unable to find the phase propagation according to SSD. However, we could extract the propagation phase by using the linear regression analysis of narrow-band phase frequency characteristics [17]. Figure 12 shows the linear regression analysis of (normalized) minimum-phase characteristics against wavenumber k, where k 200 = 2 · 200/c = 3 70 (c is the speed of sound).…”

“…The critical distance, r c [17], based on the energy rate between direct and reverberant sound is defined by…”