基于卷积神经网络的短时傅里叶变换

Short-Time Fourier Transform Based on Convolutional Neural Network

摘要: 本研究提出了一种基于卷积神经网络(CNN)的短时傅里叶变换方法，用于揭示非稳态信号的频谱随时间的变化规律。我们设计了一个卷积神经网络，采用双层结构，并随机初始化网络权重系数，不包含偏置系数。输入数据为随机生成的一维信号，其傅里叶变换作为标签数据。通过使用平方误差作为损失函数，并运用梯度下降法对网络进行训练，网络逐渐学得输入信号到其傅里叶变换的映射规则。同时，我们观察到网络权重系数在迭代过程中逐渐逼近傅里叶变换的核函数。基于学到的核函数，我们进行了信号的时频分析。数值试验结果表明，以通过训练获得的核函数作为基函数的短时傅里叶变换能取得与传统窗口傅里叶变换相一致的结果，证明了该方法的有效性。这一基于卷积神经网络的短时傅里叶变换方法为处理非稳态信号提供了一种新颖而有效的途径。

Abstract: This study proposes a windowed Fourier transform method based on the Convolutional Neural Network (CNN) to reveal the temporal evolution of the spectrum of non-stationary signals. We designed a CNN with a dual-layer structure, randomly initialized network weight coefficients, and no bias terms. The input data consists of randomly generated one-dimensional signals, with their Fourier transforms serving as label data. Using the mean square error as the loss function and applying gradient descent for network training, the network gradually learns the mapping rules from input signals to their Fourier transforms. Simultaneously, we observed that the network weight coefficients gradually approximate the Fourier transform kernel during the iterative process. Based on the learned kernel function, we conducted a time-frequency analysis of signals. Numerical experimental results demonstrate that the windowed Fourier transform obtained through the learned kernel function as basis functions achieve consistent results with the traditional windowed Fourier transform, confirming the effectiveness of the proposed method. This CNN-based windowed Fourier transform method provides a novel and effective approach for processing non-stationary signals.