# Research on the UAV Sound Recognition Method Based on Frequency Band Feature Extraction
## 2 Method and Model Establishment
### Convolutional Neural Network for Feature Recognition of UAV Sound  
In this article, the CNN is used to identify and classify the sound features of UAVs. CNN is a deep learning model and a multilayer perceptron analogous to artificial neural networks. The model training samples consist of various sound features with correctly labeled data tags. After completion of model training, hyperparameter tuning, and evaluation, the optimized acoustic model can be deployed for feature classification, recognition, and prediction. Typical CNN generally has four basic layers: a convolutional layer, an excitation layer, a pooling layer, and a fully connected layer. The convolutional layer employs convolution kernels to operate as 2-D signal filters. In CNNs, the convolution kernels are not predefined but instead optimized through backpropagation during training. The mathematical expression for 2-D discrete convolution is Equation (16). \[[f*g](x,y)=\sum_{n=-\infty}^{+\infty}\sum_{m=-\infty}^{+\infty}f(m,n)g(x-m,y-n) \tag{16}\]  
where the image data is abstracted as a 2-D discrete function \(f\), and the kernel as \(g\). The mathematical formulation of a CNN convolutional layer is Equation (17). \[Y(i,j,L)=\sum_{n=1}^{K_{h}}\sum_{m=1}^{K_{w}}G(m,n,L)X_{p}\big{[}(i-1)S_{x}+1+m,(j-1)S_{y}+1+n,L\big{]} \tag{17}\]  
Here, \(X_{p}\) represents the padded input data. \(S_{x}\) and \(S_{y}\) denote the convolution strides along the x and y axes, respectively. \(L\) accounts for additional dimensions (e.g., channels), while \(K_{h}\) and \(K_{w}\) specify the height and width of the convolution kernel. In CNN, the output dimensions can be calculated based on the input feature map size, kernel dimensions, padding amount, and stride values. The precise computational formulas are Equation (18). \[\left\{ \begin{array}{l}H_{o}=(H_{p}-K_{h}+2P)/S_{x}+1\\ W_{o}=(W_{p}-K_{w}+2P)/S_{y}+1\end{array} \right. \tag{18}\]  
where \(H_{o}\) and \(W_{o}\) represent the height and width of the output dimensions, \(H_{p}\) and \(W_{p}\) are the height and width of the input, \(K_{h}\) and \(K_{w}\) are the kernel dimensions, \(P\) is the padding size, and \(S_{x}\) and \(S_{y}\) are the strides along the x and y axes. The activation layer employs the ReLU function to introduce nonlinear mappings, enabling the network to learn and represent complex data patterns. This prevents multiple linear layers from collapsing into an equivalent single-layer system, which would severely limit model capability. Thus, an activation layer typically follows each convolutional layer. The ReLU function used in this study is defined as Equation (19). \[f(x)=\max(0,x) \tag{19}\]  
ReLU is currently the most widely adopted activation function, essentially a max operation that is non-differentiable across its entire domain. It addresses the vanishing gradient problem in the positive interval and excels in computational efficiency. For a given activation layer with function \(f(x)\), the output is computed as Equation (20). \[Y_{act}(i,j,L)=f(Y(i,j,L)) \tag{20}\]  
where \(Y\) represents the convolutional layer output, and \(Y_{act}\) denotes the activated output. Regarding the pooling layer, given an input feature map, pooling operations partition it into sub-regions and apply aggregation (e.g., maximum or average values) to each sub-region. This process can be conceptualized as sliding a window over the input feature map, where the window selects either the maximum or average value within its coverage to generate a new feature map. Pooling significantly reduces spatial dimensions, thereby decreasing computational load, improving efficiency, and mitigating overfitting. The mathematical formulation for max pooling is Equation (21). \[Y_{pool}(i,j,L)=\max_{n=(i-1)\text{P}_{i}+1}^{ip}\left\{\max_{m=(j-1)\text{P}_ {i}+1}^{ip_{n}}X(m,n,L)\right\} \tag{21}\]  
A fully connected layer converts the 2-D data from convolutional and pooling operations into one-dimensional data through fully connected mappings using weighted connections, akin to traditional neural network architectures.