The decomposition of non-stationary signals is an important and challenging
task in the field of signal time-frequency analysis. In the recent two decades,
many signal decomposition methods led by the empirical mode decomposition,
which was pioneered by Huang et al. in 1998, have been proposed by different
research groups. However, they still have some limitations. For example, they
are generally prone to boundary and mode mixing effects and are not very robust
to noise. Inspired by the successful applications of deep learning in fields
like image processing and natural language processing, and given the lack in
the literature of works in which deep learning techniques are used directly to
decompose non-stationary signals into simple oscillatory components, we use the
convolutional neural network, residual structure and nonlinear activation
function to compute in an innovative way the local average of the signal, and
study a new non-stationary signal decomposition method under the framework of
deep learning. We discuss the training process of the proposed model and study
the convergence analysis of the learning algorithm. In the experiments, we
evaluate the performance of the proposed model from two points of view: the
calculation of the local average and the signal decomposition. Furthermore, we
study the mode mixing, noise interference, and orthogonality properties of the
decomposed components produced by the proposed method. All results show that
the proposed model allows for better handling boundary effect, mode mixing
effect, robustness, and the orthogonality of the decomposed components than
existing methods.

借助卷积神经网络和残差结构以及非线性激活函数对信号进行局部平均值计算，该论文提出了一种新的非平稳信号分解方法，并相比于现有方法能更好地处理边界效应、模态混合效应、分解组件的正交性以及噪声干扰的鲁棒性，这在尚未有直接使用深度学习技术对非平稳信号进行分解的文献中具有重要意义。

RRCNN: 一种基于循环残留卷积神经网络的新型信号分解方法

RRCNN: A novel signal decomposition approach based on recurrent residue  convolutional neural network

This work introduces a wavelet neural network to learn a filter-bank
specialized to fit non-stationary signals and improve interpretability and
performance for digital signal processing. The network uses a wavelet transform
as the first layer of a neural network where the convolution is a parameterized
function of the complex Morlet wavelet. Experimental results, on both
simplified data and atmospheric gravity waves, show the network is quick to
converge, generalizes well on noisy data, and outperforms standard network
architectures.

本文介绍了一种小波神经网络，该网络能够学习一个专门适合非平稳信号的滤波器组，并提高数字信号处理的可解释性和性能。实验结果表明，该网络可以快速收敛，在噪声数据上具有良好的泛化能力，并优于标准网络架构。

可训练小波神经网络用于非平稳信号

Trainable Wavelet Neural Network for Non-Stationary Signals

This paper addresses the problem of time series forecasting for
non-stationary signals and multiple future steps prediction. To handle this
challenging task, we introduce DILATE (DIstortion Loss including shApe and
TimE), a new objective function for training deep neural networks. DILATE aims
at accurately predicting sudden changes, and explicitly incorporates two terms
supporting precise shape and temporal change detection. We introduce a
differentiable loss function suitable for training deep neural nets, and
provide a custom back-prop implementation for speeding up optimization. We also
introduce a variant of DILATE, which provides a smooth generalization of
temporally-constrained Dynamic Time Warping (DTW). Experiments carried out on
various non-stationary datasets reveal the very good behaviour of DILATE
compared to models trained with the standard Mean Squared Error (MSE) loss
function, and also to DTW and variants. DILATE is also agnostic to the choice
of the model, and we highlight its benefit for training fully connected
networks as well as specialized recurrent architectures, showing its capacity
to improve over state-of-the-art trajectory forecasting approaches.

本文提出一种针对非平稳信号和多个未来时间步长预测的时间序列预测方法 DILATE，改进了深度神经网络训练的目标函数，支持精确形状和时间变化检测，并提供了用于加速优化的自定义反向传播实现，证明了 DILATE 相较于标准的均方误差 (MSE) 损失函数和 DTW 模型的优异性能。