# Interaural Coherence Estimation for Speech Processing in Reverberant Environment
## 4 General Discussion  
Using MACtotal based on time-frequency bins with a 25-ms Hamming window, 10-ms hop length, and 512-point FFT, the optimal \(L_{\mathrm{T}}\) and \(\beta\) according to frequency were determined for each reverberation environment. Based on theoretical analysis with static locations of microphones and speaker, the direct speech has a steady value within the quasi-steady interval; thus, the IC of direct speech is close to one. The diffuse speech is an infinite sum of the reflected speech having a different propagating path; therefore, the diffuse speech between two microphones is uncorrelated in the quasi-steady interval, and the IC of diffuse speech appears close to zero. In a real environment, the speaker may move, or the position of the microphone may change. Equations (9) and (10) are expressions of reverberant speech in the interval of quasi-steady state, which was represented by 0.085-0.135 s in the simulation. Thus, when the motion of microphones and speaker is slow enough to be regarded as static in the quasi-state time scale, it is based on a proper assumption. However, the room impulse responses in the simulation were measured in the static environment, which are limited when showing the performance in the dynamic environment in this paper. To estimate the IC similar to the ideal coherence, the optimal \(L_{\mathrm{T}}\) was the average quasi-steady interval of speech, and the IC estimation was inaccurate for the section beyond the quasi-steady state of speech. The optimal \(\beta\) was the weight to compensate for the steady state in the quasi-steady interval; thus, an increase in the optimal \(\beta\) can also be seen as an increase in the quasi-steady interval length. Since the fundamental frequency differs according to gender, we assumed that the optimal parameters according to gender would differ, but this was not shown in the numerical experiment. This means that the quasi-steady interval is independent of gender, and gender was not considered when determining the optimal parameters. Figure 7: Calculation time according to speech length of reference and proposed calculation methods. In contrast, the variation in optimum parameters according to frequency was shown. The optimal \(L_{\text{T}}\) and \(\beta\) decreased as the frequency increased, and this tendency of the optimal \(\beta\) was not shown in the case of high RT\({}_{60}\). In real human speech, unvoiced sound is mainly distributed in high frequency, voiced sound is distributed in low frequency, and unvoiced sound is usually shorter than voiced sound. The quasi-steady state for unvoiced sound is shorter than that for voiced sound; hence, the quasi-steady state appears shorter at high frequency, which is the same as the tendency of the optimum parameters. This result is consistent with the theoretical analysis that the IC estimation should be applied within the quasi-steady interval. In addition, we assumed that the length of the quasi-steady state was constant according to speech regardless of the reverberation environment, but the optimal \(L_{\text{T}}\) and \(\beta\) increased, and \(\beta\) was close to one as the RT\({}_{60}\) increased in the numerical experiment. This means that the quasi-steady interval became longer as RT\({}_{60}\) increased, and the quasi-steady interval included not only direct speech but also reflections, which had a small time delay with direct speech and similar energy to that of direct speech. Moreover, it was difficult to accurately distinguish between direct and diffuse speech; thus, the IC became inaccurate, and the overall MACtotal increased as RT\({}_{60}\) increased from 0.37 s to 0.79 s using the optimal parameters, as in the numerical experiment. To sum up, for the proposed IC estimation method, it is appropriate to calculate along the quasi-steady interval; therefore, \(L_{\text{T}}\) and \(\beta\) should decrease as the frequency increases, and too large a value of RT\({}_{60}\) causes incorrect estimation of the IC.