# DeCGAN: Speech Enhancement Algorithm for Air Traffic Control
## 2 Materials and Methods
### Generator  
The generator architecture of DeCGAN is illustrated in Figure 1. Specifically designed to capture features in the time-frequency domain and generate enhanced speech signals, the generator comprises a densely connected dilated convolutional encoder, a DeConformer module, a mask decoder, and a complex decoder. The encoder first uses a densely connected dilated convolutional encoder to process the input spectrograms. After that, a DeConformer module refines the extracted features. The network then splits into two branches: one branch passes the features through a mask decoder, and the other through a complex decoder. Finally, the outputs from both decoders are merged and converted back to the time domain using an inverse short-time Fourier transform. The details of the generator architecture are shown below. In the DeCGAN model, for a given speech noise \(y\in\mathbb{R}^{L\times 1}\), its representation in the time domain is converted into the frequency domain using the STFT; in this process, a complex spectrogram \(Y_{0}\in\mathbb{R}^{T\times F\times 2}\) that encompasses both magnitude and phase information is generated, where \(T\) and \(F\) represent the time and frequency dimensions. Subsequently, power-law compression, a method used to compress the dynamic range of the magnitude spectrum so that smaller signals are relatively amplified and larger signals are slightly attenuated, is employed to derive \(Y\), the compressed spectrogram [14]:  
\[Y=|Y_{0}|^{c}e^{jY_{p}}=Y_{m}e^{jY_{p}}=Y_{r}+jY_{i}\, \tag{1}\]  
where \(Y_{m}\), \(Y_{p}\), \(Y_{r}\), and \(Y_{i}\) are the magnitude, phase, real part, and imaginary part, respectively, of the noisy spectrogram after power-law compression. The power-law compression coefficient, denoted as \({}^{c}\), is set to 0.3, in accordance with the literature [14]. This also helps stabilize neural network training by preventing excessively large or small values in the feature representation. The power-law compression of this complex spectrogram ensures that the relative importance of quieter sounds is aligned with that of louder sounds, thereby better matching human auditory perception. \(|Y_{0}|^{c}\) represents the original complex spectrogram obtained directly from the STFT, which retains the full amplitude and phase  
Figure 1: Architecture of the generator in DeCGAN. information of the input signal. In contrast, \(Y_{m}\) is derived by applying power-law compression to the magnitude component of \(\left|Y_{0}\right|^{c}\). Each variable serves a distinct purpose in this dual representation. \(\left|Y_{0}\right|^{c}\) is essential for accurate phase reconstruction and retaining the complete spectral characteristics, while \(Y_{m}\) provides a compressed magnitude that aligns better with human auditory perception and facilitates more robust network training. Together, they enable the model to separately and effectively process amplitude and phase information during the enhancement process. The compressed real component \(Y_{r}\) and imaginary component \(Y_{i}\) of the spectrogram are concatenated with the magnitude \(Y_{m}\) to create the input feature \(\{Y_{m},Y_{r},Y_{i}\}\in\mathbb{R}^{B\times T\times F\times 3}\). Here, the batch size is defined as \(B\); the batch input to the model can be denoted as \(Y_{in}\in\mathbb{R}^{B\times T\times F\times 3}\), which is the generator's input. Encoder: As shown in Figure 1, an encoder, comprising two convolutional modules and a dilated convolution module at its center, is used to extract the features \(Y_{in}\). This dilated convolution module comprises four dilated convolution blocks, with \(\{1,2,4,8\}\) as the corresponding dilation factors. Through dense residual connections, the output from each layer is directly transmitted to all subsequent convolution blocks, effectively aggregating feature information from various levels and thereby capturing the multi-level features of the spectrum.