# Interaural Coherence Estimation for Speech Processing in Reverberant Environment
## 4 General Discussion
The length of the quasi-steady interval was constant in the same reverberation environment, but the optimal \(L_{\text{T}}\) became smaller when a longer window and a longer hop length were applied. In the quasi-steady interval for 0.79 s of RT\({}_{60}\) with the same \(\beta\) as one, the time interval length of seven spectrogram bins with a 25-ms window was 85 ms, but the time interval of nine spectrogram bins with a 64-ms window was 192 ms; thus, the IC was estimated for the longer time interval. The estimation performance was relatively low when larger STFT variables were applied in the numerical experiment, which means that the calculated time interval was longer than the quasi-steady interval, and it provided incorrect IC values. The reason for the different quasi-steady intervals is that it was difficult to represent time-frequency bins of the same length as the quasi-steady interval for speech as the STFT variables became larger. On the contrary, the conventional method was affected only by the hop length because all the previous data were used; hence, the optimal \(\alpha\) appeared constant regardless of the STFT variable based on the short difference in the hop length of 6 ms. Therefore, it is very important to apply the IC estimation method proposed in this study within the time-frequency bins that match the accurate quasi-steady interval length, whereas the conventional method is not affected by window length. The performance of the conventional method and the proposed method was determined by MACtotal, and the proposed method had 0.0008, 0.0255, and 0.0524 higher MACtotal than the conventional method with the optimal \(\alpha\) when the STFT variables, which are mainly used in speech processing, were applied. The reason for this result can be elicited from the PSD estimation equation. The conventional estimation equation, which uses all the previous time data, is similar to a type of IIR filter that shows a nonlinear phase delay with respect to the frequency and distortion in comparison with the original signal. Thus, the conventional method also estimates PSD by applying an IIR filter to \(X_{i}^{*}X_{j}\), resulting in distortion in comparison to reverberation speech. The proposed method in this paper is an FIR filter type that shows a linear phase delay or zero phase delay with respect to the frequency and no distortion. The estimation of the PSD using the proposed method does not lead to distortion of the PSD; thus, it provides more accurate IC. However, in the previous numerical experiment, the proposed method accurately estimated the IC of the direct speech, but it had worse IC estimation performance of diffuse speech compared to the conventional method. This means that applying the calculation within a finite interval, as in the proposed method, was suitable for direct speech but not for diffuse speech. The FIR filter form of the proposed method with quasi-steady interval compensated for the problem of speech that is continuously varying over time; thus, it was possible to accurately estimate the IC of the direct speech. Also, it quickly reflected changes of speech; thus, the boundary bins between the direct and diffuse speech with the proposed method had more accurate IC than the conventional method. In a high-RT\({}_{60}\) environment, the energy of diffuse speech decreased slowly with respect to time; therefore, diffuse speech was also quasi-steady within the quasi-steady interval of direct speech. Since the IC of diffuse speech can appear close to one when the proposed method recognizes diffuse speech as direct speech, the estimation performance for diffuse speech was lower than that of the conventional method, as shown in the test experiment. Nevertheless, the IC of direct speech was more accurately estimated, and the overall performance was improved. Moreover, the computation time between the proposed and conventional methods was compared according to speech length.