# Big-Delay Estimation for Speech Separation in Assisted Living Environments
## 5 Results  
Anechoic stereo mixtures consisting of up to four sources were generated using randomly selected speech utterances from a total of 25,200 files in the TIMIT corpus [101]. The evaluation was carried out using a TF window with a \(K=2048\)-sample Hamming window and a 50% overlap. Algorithms 1 and 2 were implemented in MATLAB 2021a. ```
1:Find the delay estimate, \(\hat{\delta}_{j}\), using Equation (22) as per the Elevatogram [5]. 2:Subtract the delayed sources in \(\mathbf{\Lambda}_{2}\) using Equation (32). 3:Find the attenuation estimate, \(\hat{\alpha}_{j}\), using Equation (29). 4:Using the estimated (\(\hat{\alpha}_{j}\), \(\hat{\delta}_{j}\)) pairs corresponding to the sources, compute the TF mask using Equations (26) and (37). 5:Compute the ITF transform. ```  
**Algorithm 2** Elevato-DUET algorithm  
The goal is to separate \(s_{j}[n]\) from a mixture of \(J\) sources. Up to \(J=4\) source utterances were considered. To construct the Elevatogram matrix, \(\mathbf{P}\), as described in [5], the total number of quantization levels used was \(L=100\) and the number of tiles was \(\mathcal{T}\times\mathcal{T}=2\times 2\) to keep the Matlab computation time low. An analysis of the improvement obtained by increasing the tiling parameter is given in [5]. The performance of the proposed techniques was evaluated using relative delays in the range \(1\leq\delta_{j}\leq 200\) samples. The number of equally spaced azimuth positions was \(M=1000\) in the range \(0\leq g\leq 1\) for Elevato-AdRess. It was assumed that the difference in relative delay between any two pairs of sources could not be less than \(\Delta g<150\) units on the gain axis and that it should be separated by at least 40 samples of relative delay so that the peaks were sufficiently apart, and thus, were distinguishable (Figure 4). The quality of the separated speech utterances was evaluated using BSS_Eval [102] and PEASS [103] and their intelligibility was measured using Perceptual Evaluation of Speech Quality (PESQ) [104] scores. The Ideal Binary Mask (IBM) is considered the ultimate goal of Computational Auditory Scene Analysis (CASA) [105]. The target source is judged to be present at TF points where it dominates its interference. Consequently, it is preserved. In the regions where the source has a weaker presence than the interference, it is discarded. To evaluate the quality of recovered utterances, the two proposed methods were benchmarked against the IBM ([[https://github.com/IoSR-Surrey/MatlabToolbox](https://github.com/IoSR-Surrey/MatlabToolbox)]([https://github.com/IoSR-Surrey/MatlabToolbox](https://github.com/IoSR-Surrey/MatlabToolbox)), accessed on 15 April 2025) [106], which is assumed to give the best achievable separation quality. Given a sampling rate of \(F_{s}=16\) kHz, in a noiseless scenario, the two benchmark techniques achieved the following performance. DUET estimates delays of up to 7 samples. AdRess was designed for instantaneous scenarios. This is captured by the poor performance of DUET and AdRess for large relative delays in Figure 5.  
Figure 4: Speech utterances recovered from a mixture of 4 sources using Elevato-AdRess and Elevato-DUET are illustrated. The first column gives the clean speech sources. The second column shows the source estimates recovered by Elevato-AdRess. The third column presents the sources estimated by Elevato-DUET. In each figure, the unit of the normalized frequency is given on the y-axis. The primary result is that Elevato-DUET in the third column contains more interference. Speech enhancement and demixing algorithms employ various analysis and synthesis techniques, in the form of spectral energy and phase manipulation techniques, that introduce distortions, noise, and artifacts, and are typically called filtering errors [107]. In summary, measurements tend to decrease as the number of sources in the mixture increases, primarily due to the higher probability of sources overlapping in the TF bins.