# Big-Delay Estimation for Speech Separation in Assisted Living Environments
## 4 TF Masking
### Elevato-AdRess: Separation via Frequency-Azimuth Plane  
The classical AdRess algorithm [65] is often used for music demixing, particularly when the sources are mixed using a pan-pot approach. It isolates sources by localizing the IID cues on a frequency-azimuth plane. This method separates music from the TF mixture by employing a form of spectral energy cancellation technique, which uses attenuations as a spatial cue. They are obtained from the magnitude spectra, \(|\mathbf{X}_{i}[k,\tau]|\), where \(\mathbf{X}_{i}\) is the \(i^{th}\) channel mixture. The AdRess algorithm [65] was licensed for integration into Sony's SingStar game on the PlayStation 3. Subsequently, it was licensed to Rifstation, which was later acquired by Fender and utilized by millions of users between 2012 and 2018. Each source is given a position in the stereo field using an azimuth location. In the sound engineering and music production industries these panning coefficients are used to create multichannel mixtures [65; 88]. These coefficients scale the contribution of each source in each of the available channels. We extended this approach to an anechoic speech mixing model, introducing the D-AdRess technique in [83], which considers the mixing model in Equations (8) and (9). D-AdRess uses the magnitude spectra, \(|\mathbf{X}_{i}[k,\tau]|\) and the phase spectra, \(\angle\mathbf{X}_{i}[k,\tau]\). D-AdRess was restricted to scenarios with a relative delay of up to 5 samples. The primary contribution of the present paper is an extension of the AdRess technique. It extends AdRess to large delay scenarios where the delays are up to 200 samples. The resulting algorithm is called Elevato-AdRess, acknowledging its reliance on the Elevatogram for accurate estimation of large delays [5]. Elevato-AdRess is summarized in Algorithm 1. The AdRess technique has garnered widespread adoption in recent research [89; 90; 91], and has been improved in subsequent contributions [9; 84]. In addition, it has also been cited in a patent for an acoustic noise monitoring framework [92]. The proposed method, Elevato-AdRess, operates as a beamforming technique that maximizes the power of the source arriving from a specific direction, corresponding to \(\hat{\delta}_{j}\), using a pair of microphones. The Signal-to-Noise Ratio (SNR) is the ratio of the target source power to the combined power of all interfering speech sources. This approach is equivalent to maximizing the SNR, as described in [61]. The use of relative delay estimates for beamforming was reported in [93]. Prior information regarding the direction of the target and the interference helps implement robust IS techniques for speech enhancement [44]. To introduce Elevato-AdRess, we consider the two-synthetic-signal example that served as motivation in [84]. The first signal, \(s_{1}[n]\), is composed of sinusoids with frequencies, \(k_{1}=100\) Hz and \(k_{3}=300\) Hz, and the second signal, \(s_{2}[n]\), has components of frequency, \(k_{2}=200\) Hz and \(k_{3}=400\) Hz. The resulting sources\[s_{1}[n] =\sin\biggl{(}2\pi k_{1}\frac{n}{F_{s}}\biggr{)}+\sin\biggl{(}2\pi k _{3}\frac{n}{F_{s}}\biggr{)}, \tag{27}\] \[s_{2}[n] =\sin\biggl{(}2\pi k_{2}\frac{n}{F_{s}}\biggr{)}+\sin\biggl{(}2\pi k _{4}\frac{n}{F_{s}}\biggr{)}, \tag{28}\]  
are mixed via Equations (8) and (9) with the attenuation coefficients \(\alpha_{1}=0.8\) and \(\alpha_{2}=0.2\). The authors of [84] localized the IID cues on a frequency-gain plane, \(\mathbf{A}=[\mathbf{A}_{1},\mathbf{A}_{2}]\in\mathbb{R}^{K\times M}\), as illustrated in Figure 3a, by scaling \(|\mathbf{X}_{1}|\) relative to \(|\mathbf{X}_{2}|\) and vice versa, with respect to an attenuation range \(g\), where \(0\leq g\leq 1\). This range is divided into \(M\) equally spaced levels. The cancellation approach described in [5] results in the difference between the magnitudes of the Short-Time Fourier Transform (STFT) representations of the constituent sources to be zero [48].