# Amplitude and Phase Information Interaction for Speech Enhancement Method
## 3 The Proposed Method Architecture
In the final part of the Magphase unit, there is a module that facilitates the interaction of information between the magnitude and phase. The calculation formula for the elements input into this module is as follows:  
\[X_{2}^{m_{i}}=f_{p2m}\Big{(}X^{m},X_{1}^{P_{i}}\Big{)} \tag{5}\]  
\[X_{2}^{P_{i}}=f_{m2p}\Big{(}X_{1}^{P_{i}},X^{mi}\Big{)} \tag{6}\]  
where \(f_{p2m}\) represents the transfer of phase spectrum information to the magnitude spectrum, and \(f_{m2p}\) represents the transfer of magnitude spectrum information to the phase spectrum. The formula for this function is as follows:  
Figure 1:0  
where \(\cdot\) denotes element-wise multiplication between two matrices, and \(conv\) represents a \(1\times 1\) convolution. The effect of the Tanh function is to restrict the range of the output of the convolutional layer to [-1, 1], thereby introducing non-linear activation on the output of the convolutional layer and enhancing the network's expression capability. The convolutional layer performs spatial feature extraction on input data, capturing local patterns and spatial hierarchies, allowing the model to learn important features of the phase spectrum and magnitude spectrum. The magnitude spectrum contains the amplitude information of the signal, while the phase spectrum contains the phase information. By using the Magphase module to combine these two spectra, the model can simultaneously consider both amplitude and phase features. Therefore, using the combination of magnitude and phase spectra can provide a more comprehensive feature representation, thereby enhancing the capability of the model. To enable the model to learn features of both magnitude and phase in the full-band, there is a full-band module. The structure of this module, as shown in Figure 3, primarily consists of a LSTM layer with 512 hidden units. It is designed to extract the full-band information \(X_{mp}\) obtained from the output of the pMix module and output the full-band feature \(F_{mp}\), which includes both magnitude and phase information. The unfold module's specific function is to divide the full-band into sub-bands. For each frequency \(f\) in the noisy speech spectrum, it takes the corresponding frequency vector \(\overset{\rightarrow}{X_{1}^{i}}\) along the time axis. With this vector as the center, it selects \(n\) frequency vectors from both sides, resulting in a total width of \(2\times n\). For the frequency axes on the upper and lower sides of the spectrum where the surrounding frequencies are less than \(n\), the missing side's frequency axis vector is mapped to the missing part of the vector. This process generates sub-bands centered around the corresponding frequency axes. Combining all the sub-bands together forms the \(F_{sub}\) unit. The number of sub-bands in this unit is the same as the number of frequency points in the full-band spectrum, which is \(f\). The width of the sub-bands affects the model's extraction of inter-sub-band correlation features. In the model, the sub-bands are divided by taking one frequency point as the center and extending it above and below by a set length. In this paper, after performing STFT, the number of frequency points \(F\) in the spectrum is 257, which corresponds to the division of 257 sub-bands. Figure 1:1 Structure of full-band. The LSTM (hidden size = 512) block denotes a LSTM layer with 512 hidden units. In the original FullSubNet paper [11], the width of the sub-bands was set to 15. However, after conducting experiments, it was found that adjusting the width of the sub-bands resulted in better experimental results. This indicates that an appropriate sub-band width allows the model to learn sub-band features more effectively. The \(F_{sub}\) unit and the \(F_{mp}\) unit are concatenated to obtain the final value given to the sub-band unit, denoted as \(F=\left\{F_{sub},F_{mp}\right\}\). \(F\) consists of \(f+1\) independent vectors, each with a dimension of \((t,2n+1)\), where \(t\) represents the temporal length of the corresponding noisy signal.