Frequency Domain Representation Research Articles

Analyzing VEGFA/VEGFR1 Interaction: Application of the Resonant Recognition Model-Stockwell Transform Method to Explore Potential Therapeutics for Angiogenesis-Related Diseases.

The interaction between vascular endothelial growth factor A (VEGFA) and VEGF receptor 1(VEGFR1) is a central focus for drug development in pathological angiogenesis, where aberrant angiogenesis underlies various anomalies necessitating therapeutic intervention. Identifying hotspots of these proteins is crucial for developing new therapeutics. Although machine learning techniques have succeeded significantly in prediction tasks, they struggle to pinpoint hotspots linked to angiogenic activity accurately. This study involves the collection of diverse VEGFA and VEGFR1 protein sequences from various species via the UniProt database. Electron-ion interaction Potential (EIIP) values were assigned to individual amino acids and transformed into frequency-domain representations using discrete Fast Fourier Transform (FFT). A consensus spectrum emerged by consolidating FFT data from multiple sequences, unveiling specific characteristic frequencies. Subsequently, the Stockwell Transform (ST) was employed to yield the hotspots. The Resonant Recognition Model (RRM) identified a characteristic frequency of 0.128007 with an associated wavelength of 1570nm and RRM-ST identified hotspots for VEGFA (Human 36, 46, 48, 67, 71, 74, 82, 86, 89, 93) and VEGFR1 (Human 224, 259, 263, 290, 807, 841, 877, 881, 885, 892, 894, 909, 913, 1018, 1022, 1026, 1043). These findings were cross-validated by Hotspots Wizard 3.0 webserver and Protein Data Bank (PDB). The study proposes using a 1570nm wavelength for photo bio modulation to boost VEGFA/VEGFR1 interaction in the condition that is needed. It also aims to reduce VEGFA/VEGFR2 interaction, limiting harmful angiogenesis in conditions like diabetic retinopathy. Also, the identified hotspots assist in designing agonistic or antagonistic peptides tailored to specific medical requirements with abnormal angiogenesis.

Hyperspectral Anomaly Detection Using Reconstruction Fusion of Quaternion Frequency Domain Analysis.

Most existing techniques consider hyperspectral anomaly detection (HAD) as background modeling and anomaly search problems in the spatial domain. In this article, we model the background in the frequency domain and treat anomaly detection as a frequency-domain analysis problem. We illustrate that spikes in the amplitude spectrum correspond to the background, and a Gaussian low-pass filter performing on the amplitude spectrum is equivalent to an anomaly detector. The initial anomaly detection map is obtained by the reconstruction with the filtered amplitude and the raw phase spectrum. To further suppress the nonanomaly high-frequency detailed information, we illustrate that the phase spectrum is critical information to perceive the spatial saliency of anomalies. The saliency-aware map obtained by phase-only reconstruction (POR) is used to enhance the initial anomaly map, which realizes a significant improvement in background suppression. In addition to the standard Fourier transform (FT), we adopt the quaternion FT (QFT) for conducting multiscale and multifeature processing in a parallel way, to obtain the frequency domain representation of the hyperspectral images (HSIs). This helps with robust detection performance. Experimental results on four real HSIs validate the remarkable detection performance and excellent time efficiency of our proposed approach when compared to some state-of-the-art anomaly detection methods.

Towards efficient control synthesis for nonlinear wave energy conversion systems: impedance-matching meets the spectral-domain

Existing studies within the literature that focus on designing parametric energy-maximizing controllers for Wave Energy Converter (WEC) systems predominantly rely on the impedance-matching (IM) principle, originally developed for linear time-invariant systems. Alternatively, iterative optimization routines are commonly employed for nonlinear WECs. However, these approaches often face a trade-off between effectiveness in maximizing energy extraction and computational efficiency. To address this limitation, this study proposes a computationally efficient controller tuning method for analogous synthesis in the case of nonlinear WECs. The proposed approach combines a statistical linearization technique known as spectral-domain modeling with the IM principle, to synthesize a Proportional–Integrative (PI) controller for a nonlinear WEC. Furthermore, a comparison is performed with two other synthesis methods: one based on a standard (i.e. linear) frequency-domain representation of the WEC that incorporates the IM principle, and the other employing a gradient-free optimization routine applied to the nonlinear time-domain model of the WEC for PI parameter tuning through exhaustive numerical search. A discussion on the effectiveness of each tuning method in maximizing energy absorption is provided, including an appraisal of their associated computational time requirements. Numerical analyses demonstrate that the proposed method, which integrates spectral-domain modeling and IM, can achieve (almost) optimal PI controller design for a nonlinear WEC. Furthermore, this study addresses the inaccuracies inherent in the frequency-domain approach and significantly reduces the computational time compared to the exhaustive search procedure. The findings of this research represent a significant advancement towards the development of simple, effective, and efficient IM-based techniques for synthesis of controllers in nonlinear WEC systems

A Joint Time-Frequency Domain Transformer for multivariate time series forecasting

In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and frequency domain representations to make predictions. The frequency domain representation efficiently extracts multi-scale dependencies while maintaining sparsity by utilizing a small number of learnable frequencies. Simultaneously, the time domain (TD) representation is derived from a fixed number of the most recent data points, strengthening the modeling of local relationships and mitigating the effects of non-stationarity. Importantly, the length of the representation remains independent of the input sequence length, enabling JTFT to achieve linear computational complexity. Furthermore, a low-rank attention layer is proposed to efficiently capture cross-dimensional dependencies, thus preventing performance degradation resulting from the entanglement of temporal and channel-wise modeling. Experimental results on eight real-world datasets demonstrate that JTFT outperforms state-of-the-art baselines in predictive performance.

Representation modeling learning with multi-domain decoupling for unsupervised skeleton-based action recognition

Skeleton-based action recognition is one of the basic researches in computer vision. In recent years, the unsupervised contrastive learning paradigm has achieved great success in skeleton-based action recognition. However, previous work often treated input skeleton sequences as a whole when performing comparisons, lacking fine-grained representation contrast learning. Therefore, we propose a contrastive learning method for Representation Modeling with Multi-domain Decoupling (RMMD), which extracts the most significant representations from input skeleton sequences in the temporal domain, spatial domain and frequency domain, respectively. Specifically, in the temporal and spatial domains, we propose a multi-level spatiotemporal mining reconstruction module (STMR) that iteratively reconstructs the original input skeleton sequences to highlight spatiotemporal representations under different actions. At the same time, we introduce position encoding and a global adaptive attention matrix, balancing both global and local information, and effectively modeling the spatiotemporal dependencies between joints. In the frequency domain, we use the discrete cosine transform (DCT) to achieve temporal-frequency conversion, discard part of the interference information, and use the frequency self-attention (FSA) and multi-level aggregation perceptron (MLAP) to deeply explore the frequency domain representation. The fusion of the temporal domain, spatial domain and frequency domain representations makes our model more discriminative in representing different actions. Besides, we verify the effectiveness of the model on the NTU RGB+D and PKU-MMD datasets. Extensive experiments show that our method outperforms existing unsupervised methods and achieves significant performance improvements in downstream tasks such as action recognition and action retrieval.

Developing children's ASR system under low-resource conditions using end-to-end architecture

The work presented in this paper aims at enhancing the performance of end-to-end (E2E) speech recognition task for children's speech under low resource conditions. For majority of the languages, there is hardly any speech data from child speakers. Furthermore, even the available children's speech corpora are limited in terms of the number of hours of data. On the other hand, large amounts of adults' speech data are freely available for research as well as commercial purposes. As a consequence, developing an effective E2E automatic speech recognition (ASR) system for children becomes a very challenging task. One may develop an ASR system using adults' speech and then use it to transcribe children's data, but this leads to very poor recognition rates due to the stark differences in the acoustic attributes of adults' and children's speech. In order to overcome these hurdles and to develop a robust children's ASR system employing E2E architecture, we have resorted to several out-of-domain and in-domain data augmentation techniques. For out-of-domain data augmentation, we have explicitly modified adults' speech to render it acoustically similar to that of children's speech before pooling into training. On the other hand, in the case of in-domain data augmentation, we have slightly modified the pitch and duration of children's speech in order to create more data capturing greater diversity. Data augmentation approaches helps in mitigating the ill-effects resulting from the scarcity of data from child domain to a certain extent. This, in turn, reduces the error rates by a large margin. In addition to data augmentation, we have also studied the efficacy of Gamma-tone frequency cepstral coefficients (GFCC) and frequency domain linear prediction (FDLP) technique along with the most commonly used Mel-frequency cepstral coefficients (MFCC) for front-end speech parameterization. Both MFCC as well as GFCC capture and model the spectral envelope of speech. On the other hand, application of linear prediction on the frequency domain representation of speech signal helps to effectively capture the temporal envelope during front-end feature extraction. Employing FDLP features that model the temporal envelope provides important cues for the perception and understanding of stop bursts and, at times, complete phonemes. This motivated us to perform a comparative experimental study of the effectiveness of the three aforementioned front-end acoustic features. In our experimental explorations, the use of proposed data augmentation in combination of FDLP features has shown a relative improvement in character error rate by 67.6% over the baseline system. The combination of data augmentation with MFCC or GFCC features is observed to result in lower recognition performances.

TFCSRec: Time–frequency consistency based contrastive learning for sequential recommendation

Sequential recommendation aims to predict future user interactions by analyzing dynamic patterns within their historical behavior sequences. Deep neural networks have recently become popular for learning representations of these sequences in the time domain. However, representing users’ intentions in the time domain faces challenges such as noise in interactions and sparsity of data. Contrastive learning and representation learning in the frequency domain can mitigate these issues from different perspectives. In this paper, to fully integrate time-domain sequence representations, frequency-domain sequence representations and contrastive learning based on them, we propose a model called Time–Frequency Consistency based contrastive learning for Sequential Recommendation (TFCSRec). TFCSRec utilizes a time-domain encoder with a fully connected network and a filter network to extract high-order features and catch pure sequential patterns. Then, a learnable frequency-domain encoder with a recurrent neural network is designed to capture sequential characteristics in the frequency-domain space. Finally, TFCSRec combines a recommendation task and two contrastive learning tasks to optimize the two user representation encoders. Its contrastive learning is designed to minimize a contrastive regularization loss and a time–frequency consistency loss, which for the first time is constructed directly on the time-domain sequence representation and the frequency-domain sequence representation. Experiments on five benchmark datasets show that the proposed TFCSRec model outperforms other sequential recommendation models based on deep neural networks.

ИСПОЛЬЗОВАНИЕ ШТАТНОЙ ОСНАСТКИ ТОКАРНОГО СТАНКА ДЛЯ АНАЛИЗА ВИБРАЦИОННОГО ФОНА ПРОЦЕССА РЕЗАНИЯ

Predictive maintenance is a proactive maintenance strategy that uses condition monitoring tools to detect signs of damage, abnormalities, and equipment performance. The most commonly used method for rotating machines is vibration analysis. The most commonly used method for condition analysis of rotating parts is vibration analysis. Most signal analysis tools today use the fast Fourier transform (FFT), which is a special case of the generalized discrete Fourier transform and converts a vibration signal from its time domain representation to an equivalent frequency domain representation. This article focuses on the use of discrete Fourier transform for machining signal analysis.

Prediction of Particulate Matter 2.5 Concentration Using a Deep Learning Model with Time-Frequency Domain Information

In recent years, deep learning models have gained significant traction and found extensive applications in the realm of PM2.5 concentration prediction. PM2.5 concentration sequences are rich in frequency information; however, existing PM2.5 concentration prediction models lack the ability to capture the frequency information. Therefore, we propose the Time-frequency domain, Bidirectional Long Short-Term Memory (BiLSTM), and attention (TF-BiLSTM-attention) model. First, the model uses Discrete Cosine Transform (DCT) to convert the time domain information into its corresponding frequency domain representation. Second, it joins the time domain information with the frequency domain information, which enables the model to capture the frequency domain information on top of the original. Simultaneously, incorporating the attention mechanism after BiLSTM enhances the importance of critical time steps. Empirical results underscore the superior predictive performance of our proposed univariate model across all sites, outperforming both the univariate BiLSTM, univariate BiLSTM-attention, and univariate TF-BiLSTM. Meanwhile, for the multivariate model that adds PM2.5 concentration from other sites in the study area as input variables, our proposed model outperforms the prediction of some basic models such as BiLSTM and some hybrid models such as CNN-BiLSTM for all sites.

Continuous-time balanced truncation for time-periodic fluid flows using frequential Gramians

Reduced-order models for flows that exhibit time-periodic behavior (e.g., flows in turbomachinery and wake flows) are critical for several tasks, including active control and optimization. One well-known procedure to obtain the desired reduced-order model in the proximity of a periodic solution of the governing equations is continuous-time balanced truncation. Within this framework, the periodic reachability and observability Gramians are usually estimated numerically via quadrature using the forward and adjoint post-transient response to impulses. However, this procedure can be computationally expensive, especially in the presence of slowly-decaying transients. Moreover, it can only be performed if the periodic orbit is stable in the sense of Floquet. In order to address these issues, we use the frequency-domain representation of the Gramians, which we henceforth refer to as frequential Gramians. First, these frequential Gramians are well-defined for both stable and unstable dynamics. In particular, we show that when the underlying system is unstable, these Gramians satisfy a pair of allied differential Lyapunov equations. Second, they can be estimated numerically by solving algebraic systems of equations that lend themselves to heavy computational parallelism and that deliver the desired post-transient response without having to follow physical transients. The computational gains that we can achieve by using the frequency domain are demonstrated on a simple three-dimensional toy model that exhibits time-periodic dynamics. We then demonstrate this method on a periodically-forced axisymmetric jet at Reynolds numbers Re=1250 and Re=1500. At the lower Reynolds number, the flow strongly amplifies subharmonic perturbations and exhibits vortex pairing about a Floquet-stable T-periodic solution. At the higher Reynolds number, the underlying T-periodic orbit is unstable and the flow naturally settles onto a 2T-periodic limit cycle characterized by pairing vortices. At both Reynolds numbers, we compute a reduced-order model and we use it to design a feedback controller and a state estimator capable of suppressing vortex pairing.

Performance analysis of digitally controlled nonlinear systems considering time delay issues

In this paper, a comprehensive investigation into discretization, effective sample time selection considering delays in the system, and time and frequency domain analysis of a DC-DC buck converter, which plays a vital role in photovoltaic (PV) systems, is conducted to enhance the understanding of their dynamic behavior, optimize control algorithms, improve system efficiency, and ensure reliable power conversion in photovoltaic applications. To effectively address the non-linear behavior and enhance digital control of a buck converter by selecting the best sample time, several approaches can be employed. These include accurate modeling and identification of non-linear elements, development of advanced control algorithms that account for non-linearities, implementation of adaptive control techniques, and utilization of feedback mechanisms to compensate for deviations from linearity. By considering and mitigating the non-linear behavior, digital control systems can achieve improved accuracy, stability, and transient behavior in regulating the buck converter's output waveforms (voltage or current). The results of the study demonstrated that the trapezoidal integration method which is also known as bilinear approximation, or Tustin's approach outperformed other commonly used discretization methods, such as first-order hold (FOH), zero-order hold (ZOH), impulse response matching (impulse invariant), and matched pole-zero (MPZ) technique, in dual-domain (both time and frequency) analysis. The key finding highlighting the superiority of the bilinear approximation was its ability to achieve the closest match in the frequency domain bridging the continuous-time and discrete systems. This finding emphasizes the significance of the bilinear approach in preserving the frequency characteristics of the original continuous-time system during discretization. By employing this method, the discrete system closely approximated the behavior of its continuous-time counterpart, ensuring accurate frequency-domain representation.

Optimizing and Analyzing Performance of Motor Fault Diagnosis Algorithms for Autonomous Vehicles via Cross-Domain Data Fusion

Electric motors play a pivotal role in the functioning of autonomous vehicles, necessitating accurate fault diagnosis to ensure vehicle safety and reliability. In this paper, a novel motor fault diagnosis approach grounded in vibration signals to enhance fault detection performance is presented. The method involves capturing vibration signals from the motor across various operational states and frequencies using vibration sensors. Subsequently, the signals undergo transformation into frequency domain representations through fast Fourier transform. This includes normalizing and concatenating the amplitude frequency and phase frequency signals into comprehensive frequency domain information. Leveraging Gramian image-encoding attributes, cross-domain fusion of time-domain and frequency-domain data is achieved. Finally, the fused Gram angle field map is fed into the ConvMixer deep learning model, augmented by the ECA mechanism to facilitate precise motor fault identification. Experimental outcomes underscore the efficacy of cross-domain data fusion, showcasing improved pattern recognition and recognition rates for the models compared to traditional time-domain methods. Additionally, a comparative analysis of various deep learning models highlights the superior performance of the ECA-ConvMixer model. This study makes significant contributions by introducing a cross-domain data fusion method, merging time-domain and frequency-domain information to enhance motor vibration signal analysis. Additionally, the incorporation of the ECA-ConvMixer deep learning model, equipped with attention mechanisms, effectively captures critical features, thus serving as a robust tool for motor fault diagnosis. These innovations not only enhance diagnostic accuracy but also have broad applications in areas like autonomous vehicles and industry, leading to reduced maintenance expenses and enhanced equipment reliability.

Exact momentum sources for gust injection in flow simulations

Vortical gusts are unsteady flow disturbances that can affect the aerodynamic performance and stability of aircraft. Generating realistic vortical gusts in flow simulations is challenging due to the complexity and diversity of turbulence characteristics. This paper introduces a novel framework for creating vortical gusts in flow simulations using momentum sources. The method can manipulate the incoming flow with any desired divergence-free velocity perturbation at any location and avoid unwanted acoustic waves in the meanwhile. It starts from a linearized incompressible momentum equation without viscous effects. The equation has a frequency-domain representation, which is an ordinary differential equation and easy to solve. Then, several conditions are imposed to determine unknown coefficients. Expressions of source terms producing one-dimensional and two-dimensional gusts are obtained. The generated velocity field is compared to the specified gust and shows outstanding agreement. Several parameters that affect the distribution of added sources are systematically studied to find a combination that can provide optimal performance in various scenarios. Finally, the model is used to assess the aerodynamic interaction of a vortical gust and thin airfoils. The results agree well with the analytical solutions provided by the Sears model.

On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading

This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

In-situ crack and keyhole pore detection in laser directed energy deposition through acoustic signal and deep learning

Cracks and keyhole pores are detrimental defects in alloys produced by laser directed energy deposition (LDED). Laser-material interaction sound may hold information about underlying complex physical events such as crack propagation and pores formation. However, due to the noisy environment and intricate signal content, acoustic-based monitoring in LDED has received little attention. This paper proposes a novel acoustic-based in-situ defect detection strategy in LDED. The key contribution of this study is to develop an in-situ acoustic signal denoising, feature extraction, and sound classification pipeline that incorporates convolutional neural networks (CNN) for online defect prediction. Microscope images are used to identify locations of the cracks and keyhole pores within a part. The defect locations are spatiotemporally registered with acoustic signal. Various acoustic features corresponding to defect-free regions, cracks, and keyhole pores are extracted and analysed in time-domain, frequency-domain, and time-frequency representations. The CNN model is trained to predict defect occurrences using the Mel-Frequency Cepstral Coefficients (MFCCs) of the lasermaterial interaction sound. The CNN model is compared to various classic machine learning models trained on the denoised acoustic dataset and raw acoustic dataset. The validation results shows that the CNN model trained on the denoised dataset outperforms others with the highest overall accuracy (89%), keyhole pore prediction accuracy (93%), and AUC-ROC score (98%). Furthermore, the trained CNN model can be deployed into an in-house developed software platform for online quality monitoring. The proposed strategy is the first study to use acoustic signals with deep learning for insitu defect detection in LDED process.

Robust fault diagnosis of quayside container crane gearbox based on 2D image representation in frequency domain and CNN

To accurately diagnose the quayside container crane (QCC) gearbox faults, this article proposes a method that combines the frequency-domain Markov transformation field (FDMTF) and multi-branch residual convolutional neural network (MBRCNN). Firstly, the gearbox vibration signal is converted into the frequency domain to reveal the components and amplitude of signals stably and concisely. Then, the one-dimensional frequency signal is encoded into the two-dimensional image by the Markov transformation field to capture the dynamic characteristics of signals. Thirdly, the MBRCNN network is constructed, which can extract multi-scale features and alleviate the problems caused by the deep network structure. Finally, the FDMTF image is fed into the constructed MBRCNN model for pattern recognition. The effectiveness of the proposed FDMTF–MBRCNN method is verified by two case studies. In Case 1, the diagnosis results of a benchmark dataset achieve 100% accuracy, better than seven state-of-the-art methods published in recent 3 years. In Case 2, the diagnosis results of the dataset collected from a 1:4 scaled test rig achieve 98.85% accuracy, better than eleven encoding methods and four convolutional neural network methods. It also can obtain a recognition accuracy of more than 94% under the conditions of small sample, different network hyper-parameters, or variable loads, which verifies its robustness. These case studies show that the FDMTF–MBRCNN method is expected to be applied to the actual fault diagnosis of QCC gearboxes.

Emotion Recognition from Spatio-Temporal Representation of EEG Signals via 3D-CNN with Ensemble Learning Techniques

The recognition of emotions is one of the most challenging issues in human-computer interaction (HCI). EEG signals are widely adopted as a method for recognizing emotions because of their ease of acquisition, mobility, and convenience. Deep neural networks (DNN) have provided excellent results in emotion recognition studies. Most studies, however, use other methods to extract handcrafted features, such as Pearson correlation coefficient (PCC), Principal Component Analysis, Higuchi Fractal Dimension (HFD), etc., even though DNN is capable of generating meaningful features. Furthermore, most earlier studies largely ignored spatial information between the different channels, focusing mainly on time domain and frequency domain representations. This study utilizes a pre-trained 3D-CNN MobileNet model with transfer learning on the spatio-temporal representation of EEG signals to extract features for emotion recognition. In addition to fully connected layers, hybrid models were explored using other decision layers such as multilayer perceptron (MLP), k-nearest neighbor (KNN), extreme learning machine (ELM), XGBoost (XGB), random forest (RF), and support vector machine (SVM). Additionally, this study investigates the effects of post-processing or filtering output labels. Extensive experiments were conducted on the SJTU Emotion EEG Dataset (SEED) (three classes) and SEED-IV (four classes) datasets, and the results obtained were comparable to the state-of-the-art. Based on the conventional 3D-CNN with ELM classifier, SEED and SEED-IV datasets showed a maximum accuracy of 89.18% and 81.60%, respectively. Post-filtering improved the emotional classification performance in the hybrid 3D-CNN with ELM model for SEED and SEED-IV datasets to 90.85% and 83.71%, respectively. Accordingly, spatial-temporal features extracted from the EEG, along with ensemble classifiers, were found to be the most effective in recognizing emotions compared to state-of-the-art methods.

Time-Domain and Frequency-Domain Mappings of Voltage-to-Charge and Charge-to-Voltage in Capacitive Devices

In this brief, we aim to show that there are generally four possible mapping functions that can be used to map the time-domain or frequency-domain representations of an applied voltage input to the resulting time-domain or frequency-domain electrical charge output; i.e., when the capacitive device is voltage-charged. Alternatively, there are four more possible combinations when the device is current-charged. The dual relationship between each pair of functions for the case of voltage or charge input are provided in terms of single or double Fourier transforms. All eight system functions coincide with each other if and only if a constant time- and frequency-independent capacitance is considered.

Passive Amplification and Noise Mitigation of Optical Signals Through Talbot Processing

Noise is one of the rare aspects of experimental work that crosses all boundaries. It is present from scientific fields like ultrafast optical signal detection to applied fields such as image processing, or even in our day-to-day lives when we are simply trying to have a conversation in a loud room. In all these cases, incoherent, stochastic noise tends to drown a signal we aim to detect, and various techniques may need to be employed to improve the clarity of the waveform, which is characterized by the signal-to-noise ratio (SNR). Yet, considering the ubiquity of noise in scientific and technology fields, it may be surprising how few methods there exists for denoising a signal. Active amplification techniques alone cannot be employed for weak, noisy signals, since the SNR is inevitably degraded due to fundamental laws of physics, while bandpass filtering schemes necessarily lead to an attenuation of the signal. In this article, we review recent advances on the concept of passive amplification techniques based on the Talbot effect to enhance the noise properties of signals through coherent energy redistribution. We demonstrate the basic framework starting from pulse repetition rate multiplication with the Talbot effect. We then extend this theory to show the principle behind passive amplification of periodic waveforms, and then how this idea can be extended to arbitrary (generally, aperiodic) signals. Methods for passive amplification of both the time-domain and the frequency-domain representations of the signal of interest are reviewed. While here we focus on the application of the technique for optical signals in the standard telecommunication band (near wavelengths of 1550 nm), the proposed denoising scheme relies on widely available wave manipulations, such that it may offer exciting opportunities for any kind of physical wave support, such as acoustics, plasmonics and other regimes of the electromagnetic spectrum, like microwaves or X-rays.

Graph learning from band-limited data by graph Fourier transform analysis

A graph provides an effective means to represent the statistical dependence or similarity among signals observed at different vertices. A critical challenge is to excavate graphs underlying observed signals, because of non-convex problem structure and associated high computational requirements. This paper presents a new graph learning technique that is able to efficiently infer the graph structure underlying observed graph signals. The key idea is that we reveal the intrinsic relation between the frequency-domain representation of general band-limited graph signals, and the graph Fourier transform (GFT) basis. Accordingly, we derive a new closed-form analytic expression for the GFT basis, which depends deterministically on the observed signals (as opposed to being solved numerically and approximately in the literature). Given the GFT basis, the estimation of the graph Laplacian, more explicitly, its eigenvalues, is convex and efficiently solved using the alternating direction method of multipliers (ADMM). Simulations based on synthetic data and experiments based on public weather and brain signal datasets show that the new technique outperforms the state of the art in accuracy and efficiency.