Compressive sensing meets time-frequency: An overview of recent advances in time-frequency processing of sparse signals

Super-resolution techniques to simulate electronic spectra of large molecular systems

An accurate treatment of electronic spectra in large systems with a technique such as time-dependent density functional theory is computationally challenging. Due to the Nyquist sampling theorem, direct real-time simulations must be prohibitively long to achieve suitably sharp resolution in frequency space. Super-resolution techniques such as compressed sensing and MUSIC assume only a small number of excitations contribute to the spectrum, which fails in large molecular systems where the number of excitations is typically very large. We present an approach that combines exact short-time dynamics with approximate frequency space methods to capture large narrow features embedded in a dense manifold of smaller nearby peaks. We show that our approach can accurately capture narrow features and a broad quasi-continuum of states simultaneously, even when the features overlap in frequency. Our approach is able to reduce the required simulation time to achieve reasonable accuracy by a factor of 20-40 with respect to standard Fourier analysis and shows promise for accurately predicting the whole spectrum of large molecules and materials.

A Literature Review Research on Monitoring Conditions of Mechanical Equipment Based on Edge Computing

The motivation of this research is to review all methods used in data compression of collected data in monitoring the condition of equipment based on the framework of edge computing. Since a large amount of signal data is collected when monitoring conditions of mechanical equipment, namely, signals of running machines are continuously transmitted to be crunched, compressed data should be handled effectively. However, this process occupies resources since data transmission requires the allocation of a large capacity. To resolve this problem, this article examines the monitoring conditions of equipment based on edge computing. First, the signal is pre-processed by edge computing, so that the fault characteristics can be identified quickly. Second, signals with difficult-to-identify fault characteristics need to be compressed to save transmission resources. Then, different types of signal data collected in mechanical equipment conditions are compressed by various compression methods and uploaded to the cloud. Finally, the cloud platform, which has powerful processing capability, is processed to improve the volume of the data transmission. By examining and analyzing the monitoring conditions and signal compression methods of mechanical equipment, the future development trend is elaborated to provide references and ideas for the contemporary research of data monitoring and data compression algorithms. Consequently, the manuscript presents different compression methods in detail and clarifies the data compression methods used for the signal compression of equipment based on edge computing.

Time-Frequency Image Analysis and Transfer Learning for Capacity Prediction of Lithium-Ion Batteries

Energy storage is recognized as a key technology for enabling the transition to a low-carbon, sustainable future. Energy storage requires careful management, and capacity prediction of a lithium-ion battery (LIB) is an essential indicator in a battery management system for Electric Vehicles and Electricity Grid Management. However, present techniques for capacity prediction rely mainly on the quality of the features extracted from measured signals under strict operating conditions. To improve flexibility and accuracy, this paper introduces a new paradigm based on a multi-domain features time-frequency image (TFI) analysis and transfer deep learning algorithm, in order to extract diagnostic characteristics on the degradation inside the LIB. Continuous wavelet transform (CWT) is used to transfer the one-dimensional (1D) terminal voltage signals of the battery into 2D images (i.e., wavelet energy concentration). The generated TFIs are fed into the 2D deep learning algorithms to extract the features from the battery voltage images. The extracted features are then used to predict the capacity of the LIB. To validate the proposed technique, experimental data on LIB cells from the experimental datasets published by the Prognostics Center of Excellence (PCoE) NASA were used. The results show that the TFI analysis clearly visualised the degradation process of the battery due to its capability to extract different information on electrochemical features from the non-stationary and non-linear nature of the battery signal in both the time and frequency domains. AlexNet and VGG-16 transfer deep learning neural networks combined with stochastic gradient descent with momentum (SGDM) and adaptive data momentum (ADAM) optimization algorithms are examined to classify the obtained TFIs at different capacity values. The results reveal that the proposed scheme achieves 95.60% prediction accuracy, indicating good potential for the design of improved battery management systems.

Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior

By means of compressive sampling (CS), a sparse signal can be efficiently recovered from its far fewer samples than that required by the Nyquist-Shannon sampling theorem. However, recovering a speech signal from its CS samples is a challenging problem, as it is not sparse enough on any existing canonical basis. To solve this problem, we propose a method which combines the approximate message passing (AMP) and Markov chain that exploits the dependence between the modified discrete cosine transform (MDCT) coefficients of a speech signal. To reconstruct the speech signal from CS samples, a turbo framework, which alternately iterates AMP and belief propagation along the Markov chain, is utilized. In addtion, a constrain is set to the turbo iteration to prevent the new method from divergence. Extensive experiments show that, compared to other traditional CS methods, the new method achieves a higher signal-to-noise ratio, and a higher perceptual evaluation of speech quality (PESQ) score. At the same time, it maintaines a better similarity of the energy distribution to the original speech spectrogram. The new method also achieves a comparable speech enhancement effect to the state-of-the-art method.

A software companion for compressively sensed time-frequency processing of sparse nonstationary signals

Compressive sensing is a computational framework for acquisition and processing of sparse signals at sampling rates below the rates mandated by the Nyquist sampling theorem. In this paper, we present seven MATLAB functions for compressive sensing based time-frequency processing of sparse nonstationary signals. These functions are developed to reproduce figures in our companion review paper.