## 4 Experimental Results
### Speech Denoising Method  
The spectral estimate of the speech signal \(\hat{S}(\eta,\Omega)\) is obtained by  
\[\hat{S}(\eta,\Omega)=g(\eta,\Omega)\cdot Y(\eta,\Omega) \tag{28}\]  
where \(g(\eta,\Omega)\) denotes a gain factor. It can be expressed by  
\[g(\eta,\Omega)=\left\{\begin{array}{ll}\left(1-\alpha\cdot \left[\frac{|\hat{D}(\eta,\Omega)|}{|Y(\eta,\Omega)|}\right]^{2}\right)^{\frac{ 1}{2}}&,\,\text{if}\Bigg{[}\frac{|\hat{D}(\eta,\Omega)|}{|Y(\eta,\Omega)|} \Bigg{]}^{2}<\frac{1}{\alpha+\beta}\\ \left(\beta\cdot\left[\frac{|\hat{D}(\eta,\Omega)|}{|Y(\eta,\Omega)|} \right]^{2}\right)^{\frac{1}{2}}&,\,\text{otherwise}.\end{array}\right. \tag{29}\]  
where \(\alpha\) and \(\beta\) represent the over-subtraction factor and spectral floor factor. They can be calculated by [17]  
\[\alpha(\eta,\Omega)=\frac{\alpha_{\text{max}}-\alpha_{\text{min}}}{T_{\text{ min}}(\eta)-T_{\text{max}}(\eta)}\cdot\left[T(\eta,\Omega)-T_{\text{min}}(\eta) \right]+\alpha_{\text{max}} \tag{30}\]  
and  
\[\beta(\eta,\Omega)=\frac{\beta_{\text{max}}}{T_{\text{min}}(\eta)-T_{\text{ max}}(\eta)}\cdot\left[T(\eta,\Omega)-T_{\text{min}}(\eta)\right]+\beta_{\text{max}} \tag{31}\]  
where the values of \(\alpha_{\text{min}}\), \(\alpha_{\text{max}}\) and \(\beta_{\text{max}}\) are empirically chosen as 1, 6 and 0.02, respectively [17], \(T(\eta,\Omega)\) is the noise masking threshold (NMT). \(T_{\text{max}}(\eta)\) and \(T_{\text{min}}(\eta)\) denote the maximum value and minimum value of the NMT in the \(\eta^{th}\) frame, respectively.  
In (29), this gain factor is one of the most flexible forms of subtractive-type algorithm. This factor allows for a variation of the tradeoff between noise reduction, residual noise and speech distortion by adequately controlling the values of the free parameters \(\alpha\) and \(\beta\). Moreover, the quantity of musical residual noise can be reduced significantly by the consideration of noise masking threshold as given in (30) and (31). Thus, the gain factor given in (29) is employed for speech denoising.  
A two-step-decision-directed (TSDD) algorithm [18] is employed to estimate the spectra of speech \(\widetilde{S}(\eta,\Omega)\), given as  
\[\widetilde{S}(\eta,\Omega)=g^{TSDD}(\eta,\Omega)\cdot Y(\eta,\Omega) \tag{32}\]  
where  
\[g^{TSDD}(\eta,\Omega)=\frac{g^{DD}(\eta,\Omega)\cdot\gamma_{post}(\eta,\Omega )}{1+g^{DD}(\eta,\Omega)\cdot\gamma_{post}(\eta,\Omega)} \tag{33}\]  
where \(\gamma_{post}(\eta,\Omega)\) and \(g^{DD}(\eta,\Omega)\) respectively represent the a posteriori SNR and a decision-directed gain factor, given as  
\[\gamma_{post}(\eta,\Omega)=\frac{|Y(\eta,\Omega)|^{2}}{E\{|D(\eta,\Omega)|_{2 }\}} \tag{34}\]  
\[g^{DD}(\eta,\Omega)=\frac{\hat{\gamma}_{priori}(\eta,\Omega)}{1+\hat{\gamma}_ {prio}(\eta,\Omega)} \tag{35}\]  
where \(\hat{\gamma}_{prio}(\eta,\Omega)=E\big{\{}\big{|}\hat{S}(\eta,\Omega)\big{|}_ {2}\big{\}}/E\big{\{}\big{|}\hat{D}(\eta,\Omega)\big{|}_{2}\big{\}}\), \(\hat{D}(\eta,\Omega)\) is the estimated spectrum of noise. \(E\) is the expectation operator.  
In (32), the estimated spectrum of speech \(\widetilde{S}(\eta,\Omega)\) is only utilized for the computation of the NMT. Detailed procedures for the computation of the NMT can be found in [19]. The denoised speech signal is obtained by  
\[\hat{s}(\eta,v)=F^{-1}[|\hat{S}(\eta,\Omega)|\cdot\exp(j\text{arg}Y(\eta, \Omega))] \tag{36}\]  
where \(F^{-1}\) denotes the operator of the inverse Fourier transform.