## 3 Methodology of TSDCA-BA Model
### Lightweight Inference Procedure  
Speech signals generally exhibit stronger energy in the low-frequency band and weaker energy in the high-frequency band. To balance the feature distribution and enhance the high-frequency components, a pre-emphasis process was applied to the input audio during both training and inference, as illustrated in Figure 1. Specifically, a high-pass filter was used to boost the high-frequency parts. The discrete-time form of the first-order high-pass pre-emphasis filter is given by Equation (2), where \(x[n]\) denotes the original speech signal,  
Figure 5: The overall architecture of the proposed Squeeze excitation Module.  
\(x^{\prime}[n]\) represents the pre-emphasized signal, and \(\alpha\) is the pre-emphasis coefficient, typically ranging from 0.95 to 0.97.  
\[x^{\prime}[n]=x[n]-\alpha\cdot x[n-1],\quad\alpha=0.97 \tag{2}\]  
To simultaneously capture the global and local spectral features of speech, multi-scale short-time Fourier transform (STFT) was employed for feature extraction. Specifically, two configurations with frame lengths of 512 and 256 were used to extract spectral features at different temporal resolutions. Each scale applied the Hann window function to facilitate the model in effectively acquiring both coarse-grained and fine-grained spectral information.  
In the inference stage, the log-magnitude spectrogram \(\mathbf{X}_{\text{log}}\in\mathbb{R}^{F\times T}\) is first normalized by its mean \(\mu\) and standard deviation \(\sigma\), as shown in Equation (3), where \(F\) is the number of frequency bins and \(T\) is the number of time frames:  
\[\tilde{\mathbf{X}}_{\text{log}}=\frac{\mathbf{X}_{\text{log}}-\mu}{\sigma} \tag{3}\]  
Here, \(\tilde{\mathbf{X}}_{\text{log}}\) is the normalized log-magnitude spectrogram; \(\mu\) and \(\sigma\) are the mean and standard deviation of \(\mathbf{X}_{\text{log}}\).  
The normalized feature \(\tilde{\mathbf{X}}_{\text{log}}\) is fed into the pretrained model \(\mathcal{M}\) to produce a time-frequency mask \(\mathbf{M}\in[0,1]^{F\times T}\) for noise suppression, as described in Equation (4):  
\[\mathbf{M}=\mathcal{M}(\tilde{\mathbf{X}}_{\text{log}}) \tag{4}\]  
where \(\mathbf{M}\) is the predicted mask applied element-wise to attenuate noise.  
The mask \(\mathbf{M}\) is applied to the linear-scale magnitude spectrogram \(\mathbf{A}=\exp(\mathbf{X}_{\text{log}})-1\), converting back from log scale as in Equation (5):  
\[\hat{\mathbf{A}}=\mathbf{A}\odot\mathbf{M} \tag{5}\]  
Here, \(\hat{\mathbf{A}}\) is the estimated clean magnitude spectrogram and \(\odot\) denotes element-wise multiplication.  
Using the phase \(\mathbf{\Phi}\in\mathbb{R}^{F\times T}\) extracted from the main scale STFT, the complex spectrogram \(\hat{\mathbf{S}}\) is reconstructed by Equation (6):  
\[\hat{\mathbf{S}}=\hat{\mathbf{A}}\odot e^{i\mathbf{\Phi}} \tag{6}\]  
where \(j\) is the imaginary unit and \(\mathbf{\Phi}\) the phase of the noisy input.  
Finally, the enhanced time-domain signal \(\hat{s}_{\text{norm}}[n]\) is recovered by ISTFT and amplitude normalization, shown in Equation (7):  
\[\hat{s}_{\text{norm}}[n]=\frac{\text{ISTFT}(\hat{\mathbf{S}})}{\text{max}(| \text{ISTFT}(\hat{\mathbf{S}})|)+\epsilon} \tag{7}\]  
where \(\epsilon\) is a small constant to avoid division by zero, and \(n\) indexes the time-domain samples.