Non-stationary signals: optimal sampling and instantaneous bandwidth estimation

Nonstationary signal (NSS) reconstruction from Time Varying (TV) coefficients of Time Varying Autoregressive (TVAR) process is presented in this paper. The proposed method consists of three steps, where in the first step, initial values for TVAR coefficients are estimated from synaptic weights of a three layer Artificial Neural Network (ANN) which is trained using Backpropagation (BP) learning algorithm. The estimated TVAR coefficients are then optimized using a Genetic Algorithm optimization algorithm for more accurate values in the second step. And finally once the TVAR coefficients are estimated using ANN and GA, it is then used to recover the original signal. Performance of proposed method has been evaluated by comparing reconstruction of various computer generated NSS from proposed methods with other methods. Five performance metrics was used for comparison where proposed method is shown to overcome the performance of other methods.

The acquisition of high-quality multi-dimensional nuclear magnetic resonance (NMR) spectra can be accelerated through the implementation of non-uniform sampling (NUS) and the employment of reconstruction method. However, the optimization of the NUS scheme and the reconstruction method have been performed independently up to now. This results in a weakened relationship between the NUS scheme and the reconstruction method and thus suboptimal reconstructed spectra, leading to shortcomings such as lost peaks and artifacts. Here, a deep learning network for jointly optimized sampling and reconstruction, referred to as JOSR-Net, is proposed. It integrates the sampling sub-network and the reconstruction sub-network into a unified end-to-end framework, aiming to simultaneously optimize both the sampling scheme and the reconstruction of undersampled data during the training process. This enables the optimal co-adaptation between the NUS scheme and the reconstruction algorithm, ultimately achieving high quality spectral reconstruction. And the results on protein spectra demonstrate that the proposed method effectively learns optimal sampling schemes and achieves superior reconstruction performance, compared to both traditional reconstruction methods and current deep learning reconstruction methods.

The development of wireless technology in recent years has increased the demand for channel resources within a limited spectrum. The system's performance can be improved through bandwidth optimization, as the spectrum is a scarce resource. To reconstruct the signal, given incomplete knowledge about the original signal, signal reconstruction algorithms are needed. In this paper, we propose a new scheme for reducing the effect of adding additive white Gaussian noise (AWGN) using a noise reject filter (NRF) on a previously discussed algorithm for baseband signal transmission and reconstruction that can reconstruct most of the signal’s energy without any need to send most of the signal’s concentrated power like the conventional methods, thus achieving bandwidth optimization. The proposed scheme for noise reduction was tested for a pulse signal and stream of pulses with different rates (2, 4, 6, and 8 Mbps) and showed good reconstruction performance in terms of the normalized mean squared error (NMSE) and achieved an average enhancement of around 48%. The proposed schemes for signal reconstruction and noise reduction can be applied to different applications, such as ultra-wideband (UWB) communications, radio frequency identification (RFID) systems, mobile communication networks, and radar systems.

Molecular communication (MC) is an important nanoscale communication paradigm, which is employed for the interconnection of the nanomachines (NMs) to form nanonetworks. A transmitter NM (TN) sends the information symbols by emitting molecules into the transmission medium and a receiver NM (RN) receives the information symbols by sensing the molecule concentration. In this paper, a model of how an RN measures and reconstructs the molecular signal is proposed. The signal around the RN is assumed to be a Gaussian random process instead of the less realistic deterministic approach. After the reconstructed signal is derived as a doubly stochastic poisson process, the distortion between the signal around the RN and the reconstructed signal is derived as a new performance parameter in MC systems. The derived distortion, which is a function of system parameters such as RN radius, sampling period, and the diffusion coefficient of the channel, is shown to be valid by employing random walk simulations. Then, it is shown that the original signal can be satisfactorily reconstructed with a sufficiently low level of distortion. Finally, optimum RN design parameters, namely, RN radius, sampling period, and sampling frequency, are derived by minimizing the signal distortion. The simulation results reveal that there is a trade‐off among the RN design parameters which can be jointly set for a desired signal distortion.

An approach based on the singular spectrum decomposition (SSD)-singular value decomposition (SVD) and frequency weight energy operator (FWEO) was proposed for early fault diagnosis of rolling bearings. Since the interference of heavy noise in the early stage of bearing fault, SSD could eliminate abundant noise, meanwhile adaptively decompose the nonlinear, non-stationary signals into multiple mono-components which had distinct physical meanings. Subsequently, SVD was adopted for de-noising in every mono-components because the noise was distributed throughout the frequency domain. In the following, signal reconstruction was performed based on the selected mono-components with de-noising. Finally, FWEO was employed for envelop analysis and the early fault diagnosis of the rolling bearing is realized. Two groups of experiment data concerning signals of early bearing fault were investigated to valid the effectiveness of the proposed method, and good fault identification effects were obtained.

Pseudo-LiDAR based stereo 3D detectors have gained popularity due to their high accuracy. However, these methods need dense depth supervision and suffer from inferior speed. To solve these two issues, a recently introduced RTS3D builds an efficient 4D feature-consistency embedding (FCE) space for the object intermediate representation without depth supervision, where FCE space performs uniform sampling to generate feature sampling points, which ignores the importance of different object regions. In this paper, we observe that, compared with the inner region, the outer region of the object plays a more important role for accurate 3D detection. To fully exploit the useful information from the outer region, we propose a novel shape-aware non-uniform sampling strategy. Instead of uniform sampling, our proposed non-uniform sampling strategy performs dense sampling in outer region and sparse sampling in inner region. Therefore, more points are sampled from the outer region and more useful features are extracted for 3D detection. In addition, we design a high-level semantic enhanced FCE module to exploit more contextual information and suppress noise better. As a result, it further improves feature discrimination of each sampling point. Experimental results on the KITTI dataset show the effectiveness of the proposed method. Compared with the baseline RTS3D, our proposed method has 2.57% improvement on car AP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{3d}$ </tex-math></inline-formula> almost without extra network parameters. Moreover, our proposed method outperforms the state-of-the-art methods without extra supervision at a real-time speed.

A technique is presented for the reconstruction of signals that suffered sampling-frequency decimation. Two assumptions are made: the original signal has to be repetitive, and no anti-aliasing filter has been used before frequency decimation. The performance of the technique is assessed by using test signals of which the original signal is known.

A sparsity adaptive compressed signal reconstruction based on sensing dictionary

In the compressive sampling theory, a small number of random linear projections of a sparse or compressible signal have contained sufficient information and the original signal can be accurately reconstructed by taking advantage of modern optimization algorithms. We proposed an approximate l 0 norm based signal reconstruction algorithm in this paper. It not only can convert the classical constrained l 0 minimization problem of the compressive sampling theory into an unconstrained optimization problem, but also can reduce the dimension of the search space substantially. The experiment results have shown that our proposed algorithm can improve the sparse signal reconstruction performance while maintaining appropriate signal reconstruction efficiency.

In addressing the problem of low prediction accuracy in the remaining useful life (RUL) prediction of rolling bearings, caused by noise interference and insufficient extraction of sensitive features by deep learning models, this paper presents a life prediction method based on signal reconstruction and dual-channel network fusion. First, addressing the issue of extracting weak features from rolling bearing vibration signals, an optimized combination of variational mode decomposition (VMD) and Teager–Kaiser energy operator (TKEO) for signal reconstruction is proposed. TKEO is used to track the energy of high-frequency impulses in the original signal. The sparrow search algorithm is employed for optimizing VMD to perform high-frequency filtering, resulting in an optimized impulse energy signal. This signal is then multiplied with the original signal to enhance weak impulse features under noisy background. Next, a dual-channel network model for RUL prediction is constructed based on temporal convolutional network (TCN) and convolutional neural networks (CNNs). The one-dimensional time-series signal obtained after reconstruction and denoising serves as the input for the TCN network channel. Simultaneously, the signal obtained after reconstruction and denoising undergoes synchrosqueezed wavelet transforms to generate a two-dimensional time–frequency representation as input for the CNN network channel. This setup allows TCN and CNN to respectively extract temporal features from the vibration signal and time–frequency features from the spectrogram. By incorporating self-attention mechanisms, internal correlations between different features are fully explored, thereby enhancing prediction accuracy.

Industrial intelligent diagnosis is a core task for ensuring the reliability and safety of mechanical equipment operation. However, traditional Transformer models have problems such as weak ability to model local time-frequency features, scattered focus on key features, and insufficient frequency sensitivity when dealing with non-stationary industrial signals, which pose many challenges in fault detection and classification. In addition, existing methods that combine discrete wavelet transform (DWT) with deep learning models often adopt a "preprocessing-classification" sequential approach. This involves first performing wavelet decomposition on the original signal and then inputting the results into a classification network for training. Such methods exhibit a disconnection between feature extraction and classification, making it challenging to achieve end-to-end optimization. This paper introduces a novel WET-BiLSTM model, whose primary innovation lies in designing DWT as a differentiable embedded module that is seamlessly integrated with Transformer and BiLSTM architectures. This design facilitates the construction of a truly end-to-end intelligent diagnostic framework.The design not only leverages self-attention for global dependency modeling but also integrates the time-frequency multi-scale decomposition capabilities of DWT with the local smoothing and recursive sequence modeling abilities of BiLSTM. This combination enables a more effective capture of critical fault information. The entire process facilitates an end-to-end mapping from the original vibration signal to the fault type, thereby eliminating the disconnect between preprocessing and model training commonly found in traditional methods. To verify the effectiveness of the proposed method, experiments are conducted on two typical industrial fault datasets, namely rolling bearing and reciprocating compressors. The results showed that WET-BiLSTM outperformed other models in terms of fault identification accuracy, stability and noise resistance. Further attention visualization analysis shows that the introduction of the DWT module enables the model to allocate more concentrated and discriminative attention weights at critical timing positions, improving the interpretability and fault awareness of the model. The study provides an efficient, reliable and physically explainable solution for the intelligent diagnosis of complex industrial equipment.

The diagnosis of compound-fault is always a difficult point, and there is not an effective method in equipment diagnosis field, and then a new method of compound-fault diagnosis was presented in the paper. The vibration signals at start-up in the gearbox are non-stationary signals, in order to solve the compound-fault diagnosis of rolling bearing, the order tracking wavelet packet and rough sets theory are combined and introduced into the fault diagnosis field. Firstly, the non-stationary vibration signals at start-up were resampled using computer order tracking arithmetic and equal angle distributed vibration signals were obtained, and then the signals were decomposed and recomposed with the wavelet packet. The energy distribution of every frequency band was calculated according to normalization process. A new feature vector can be obtained, then clear and concise decision rules can be obtained by rough sets theory. Finally, the result of compound-fault example proves that the proposed method has high validity and more amplitude appliance foreground.

The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomnographic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. The use of different mother wavelets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

The wavelet transform is a practical method for multiresolution analysis. Previously, methods for describing the transformed signal using zero-crossing information and additional complementing information (zero-crossing representation) have been studied. The zero-crossing representation, however, presents problems in that the physical interpretation of the applied additional information is not clear, and reconstruction of the original signal from the zero-crossing representation involves iterations of nonlinear operations. Other problems include the fact that extension to the multidimensional case is difficult and that the computational complexity is considerable. In this paper, the authors propose a new zero-crossing representation that uses the additional information with clear physical interpretation and has a form that is easy to handle in signal processing. A method is proposed to reconstruct the original signal from the zero-crossing representation. The method uses iterative linear operations with a theoretical guarantee of convergence and has lower computional complexity than the conventional method. The proposed zero-crossing representation is extended to the two-dimensional case and is applied to an actual image. It is experimentally verified that the reconstructed image is a good approximation to the original signal. Furthermore, the amount of additional information in the zero-crossing representation is reduced. The quality degradation of the reconstructed image is examined. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 68–78, 1999

There are three steps for compressive sensing, such as the sparse representation of signal, the design of observation matrix and the reconstruction of signal. The existing observation matrix may lose the part information of the original signal after compressing and sampling. Then, the adaptive observation matrix is proposed to sparse samples for ultrasonic wave signals that are analysed in the phased array structural health monitoring. The matrix is generated adaptively according to the information of the sparse coefficients vector, so that the sparse signal can include all the information of the original signal after compressing and sampling. Moreover, the orthogonal matching pursuit (OMP) algorithm will be used in reconstructing the ultrasonic wave signal with high probability. Finally, experiments were carried out on the aluminium plate. The proposed method that based on the adaptive observation matrix can effectively reduce the reconstruction error and more accurately and completely reconstruct the sensor response signal.