Frequency Domain Representation Research Articles

An Alignment‐Agnostic Methodology for the Analysis of Designed Separations Data

ABSTRACTChemical separations data are typically analyzed in the time domain using methods that integrate the discrete elution bands. Integrating the same chemical components across several samples must account for retention time drift over the course of an entire experiment as the physical characteristics of the separation are altered through several cycles of use. Failure to consistently integrate the components within a matrix of samples and variables creates artifacts that have a profound effect on the analysis and interpretation of the data. This work presents an alternative where the raw separations data are analyzed in the frequency domain to account for the offset of the chromatographic peaks as a matrix of complex Fourier coefficients. We present a generalization of the factorization, permutation testing, and visualization steps in ANOVA‐simultaneous component analysis (ASCA) to handle complex matrices and use this method to analyze a synthetic dataset with known significant factors and compare the interpretation of a real dataset via its peak table and frequency domain representations.

Learning multi-axis representation in frequency domain for medical image segmentation

Learning multi-axis representation in frequency domain for medical image segmentation

Real-Time Identification of Yarn Irregularities on DTY Machine Through Vibration Monitoring

This paper presents an innovative real-time monitoring system for detecting yarn irregularities during the draw texturing process in DTY machine. The system uses advanced sensors to continuously measure vibration signals, which are then analyzed for anomalies. The system incorporates advanced sensors, controllers, and embedded software for monitoring the vibrations produced during the draw texturing process. Fast Fourier Transform (FFT) in LabVIEW converts these vibration signals into their frequency-domain representation. This helps identify anomalies that could indicate potential yarn irregularities. The results from the sensor data clearly indicate that amplitude values serve as a reliable measure for detecting yarn irregularities. For normal spindles, the amplitude ranges from 10.9 to 12.2 m/s², while abnormal spindles show significantly higher values, between 31.9 and 44.3 m/s². This distinction facilitates real-time classification of yarn quality. The system's ability to identify these amplitude variations promptly can significantly reduce waste and enhance quality control. Future developments will focus on integrating an intelligent early warning system that alerts operators immediately upon detecting irregularities, enabling quicker interventions and minimizing downtime.

A Method for Correcting the Shock Response Spectrum in Missile-Borne Products

Abstract Missile-borne products often encounter shock signals that include low-frequency interference. Following the detonation of initiating devices, the displacement and velocity values are non-zero, and the acceleration signal exhibits baseline drift. This phenomenon distorts the results of Shock Response Spectrum (SRS) analysis. To address these issues, we propose an enhanced method of SRS analysis based on Variational Mode Decomposition (VMD). This method uses VMD to preprocess the shock signal by decomposing it into multiple modal components. It then eliminates modes dominated by low-frequency interference based on the correlation coefficients of the positive and negative response spectra to correct the signal. The corrected signal is analyzed using SRS, and a standard spectrum type for testing is defined. Simulations demonstrate the effectiveness and accuracy of this method, showing that it can precisely eliminate low-frequency components that interfere with the signal. The revised impulse response spectrum significantly enhances both the time-domain and frequency-domain representations of the signal. By analyzing the signal measured from a missile-borne product during the launch of specific ammunition, the method is validated, effectively resolving the SRS distortion issues caused by baseline drift. This method proves to be highly valuable for analyzing the shock environments of missile-borne product and in developing test spectrums.

Thermodynamically consistent modeling of viscoelastic solids under finite strain

The present article is concerned with modeling the viscoelastic behavior of Polydimethylsiloxane (PDMS) in large-strain regime. Starting from the basic principles of thermodynamics, an incremental variational formulation is derived. Within this model, the free energy density and dissipation function determine elastic and viscous properties of the solid. The main contribution of this paper is the estimation of the parameters in the proposed phenomenological model from measurements conducted on Sylgard184 samples. This non-linear material model simplifies to a Prony-series representation in frequency domain in case of small deformations. The coefficients of this Prony-series are detected from dynamical temperature mechanical analysis measurements. Time-temperature superposition allows to combine measurements at different temperatures, such that a sufficiently large frequency range is available for subsequent fitting of Prony-parameters. A set of material parameters is thus provided. The incremental variational formulation directly lends itself to finite element discretization, where an efficient and stable choice of elements is proposed for radially symmetric problems. This formulation allows to verify the proposed model against experimental data gained in ball-drop experiments.

Evaluation of the Use of the Angular Domain and Order Domain in a Bearing Fault Detection Framework using Deep Learning

Bearing failures are very common in the industrial environment, requiring effective fault detection methods, which can be categorized into physics-based, knowledge-based and data-driven types. Data-driven methods are efficient in differentiating healthy conditions from faulty conditions by characterizing machine signals, involving stages of data acquisition, feature extraction, and condition determination. Traditionally, feature extraction and condition determination were manual, but advances in artificial intelligence and machine learning, especially deep learning, have automated this process. Although deep learning automatically learns the best features from the input data, the signal domain can influence the model's performance. Time and frequency domain representations are widely used in fault detection methodologies using vibration signals, while angular and order domains are more common in variable operating conditions, but direct use of these domains with deep learning is still rare in the literature. Considering this, this study evaluates a bearing fault detection methodology using vibration signals in different domains (time, frequency, angular, and order) under various rotational conditions. Three distinct approaches were tested to assess the effectiveness of these representations. The results indicated that the frequency domain representation had the best overall performance and the study concluded that the angular and order domains do not offer significant advantages compared to the frequency domain. Nonetheless, it is recommended to conduct a more in-depth analysis with more diverse datasets, especially those containing early-stage bearing fault signals.

Phase Space Formulation of Light Propagation on Tilted Planes

The solution of the Helmholtz equation describing the propagation of light in free space from a plane to another can be described by the angular spectrum operator, which acts in the frequency domain. Many applications require this operator to be generalized to handle tilted source and target planes, which has led to research investigating the implications of these adaptations. However, the frequency domain representation intrinsically limits the understanding the way the signal is transformed through propagation. Instead, studying how the operator maps the space–frequency components of the wavefield provides essential information that is not available in the frequency domain. In this work, we highlight and exploit the deep relation between wave optics and quantum mechanics to explicitly describe the symplectic action of the tilted angular spectrum in phase space, using mathematical tools that have proven their efficiency for quantum particle physics. These derivations lead to new algorithms that open unprecedented perspectives in various domains involving the propagation of coherent light.

FSH3D: 3D Representation via Fibonacci Spherical Harmonics

AbstractSpherical harmonics are a favorable technique for 3D representation, employing a frequency‐based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are non‐uniform on spherical surfaces and exhibit local anisotropy, a common limitation in existing spherical harmonic decomposition methods. This paper proposes a 3D representation method using Fibonacci Spherical Harmonics (FSH3D). We introduce a spherical Fibonacci grid (SFG), which is more uniform than equiangular grids for SHT in the frequency domain. Our method employs analytical weights for SHT on SFG, effectively assigning sampling errors to spherical harmonic degrees higher than the recovered band‐limited function. This provides a novel solution for spherical harmonic transformation on non‐equiangular grids. The key advantages of our FSH3D method include: 1) With the same number of sampling points, SFG captures more features without bias compared to equiangular grids; 2) The root mean square error of 32‐degree spherical harmonic coefficients is reduced by approximately 34.6% for SFG compared to equiangular grids; and 3) FSH3D offers more stable frequency domain representations, especially for rotating functions. FSH3D enhances the stability of frequency domain representations under rotational transformations. Its application in 3D shape reconstruction and 3D shape classification results in more accurate and robust representations. Our code is publicly available at https://github.com/Miraclelzk/Fibonacci-Spherical-Harmonics.

Multi-Task Diffusion Learning for Time Series Classification

Current deep learning models for time series often face challenges with generalizability in scenarios characterized by limited samples or inadequately labeled data. By tapping into the robust generative capabilities of diffusion models, which have shown success in computer vision and natural language processing, we see potential for improving the adaptability of deep learning models. However, the specific application of diffusion models in generating samples for time series classification tasks remains underexplored. To bridge this gap, we introduce the MDGPS model, which incorporates multi-task diffusion learning and gradient-free patch search (MDGPS). Our methodology aims to bolster the generalizability of time series classification models confronted with restricted labeled samples. The multi-task diffusion learning module integrates frequency-domain classification with random masked patches diffusion learning, leveraging frequency-domain feature representations and patch observation distributions to improve the discriminative properties of generated samples. Furthermore, a gradient-free patch search module, utilizing the particle swarm optimization algorithm, refines time series for specific samples through a pre-trained multi-task diffusion model. This process aims to reduce classification errors caused by random patch masking. The experimental results on four time series datasets show that the proposed MDGPS model consistently surpasses other methods, achieving the highest classification accuracy and F1-score across all datasets: 95.81%, 87.64%, 82.31%, and 100% in accuracy; and 95.21%, 82.32%, 78.57%, and 100% in F1-Score for Epilepsy, FD-B, Gesture, and EMG, respectively. In addition, evaluations in a reinforcement learning scenario confirm MDGPS’s superior performance. Ablation and visualization experiments further validate the effectiveness of its individual components.

Structural tensor and frequency guided semi-supervised segmentation for medical images.

The method of semi-supervised semantic segmentation entails training with a limited number of labeled samples alongside many unlabeled samples, aiming to reduce dependence on pixel-level annotations. Most semi-supervised semantic segmentation methods primarily focus on sample augmentation in spatial dimensions to reduce the shortage of labeled samples. These methods tend to ignore the structural information of objects. In addition, frequency-domain information also supplies another perspective to evaluate information from images, which includes different properties compared to the spatialdomain. In this study, we attempt to answer these two questions: (1) is it helpful to provide structural information of objects in semi-supervised semantic segmentation tasks for medical images? (2) is it more effective to evaluate the segmentation performance in the frequency domain compared to the spatial domain for semi-supervised medical image segmentation? Therefore, we seek to introduce structural and frequency information to improve the performance of semi-supervised semantic segmentation for medicalimages. We present a novel structural tensor loss (STL) to guide feature learning on the spatial domain for semi-supervised semantic segmentation. Specifically, STL utilizes the structural information encoded in the tensors to enforce the consistency of objects across spatial regions, thereby promoting more robust and accurate feature extraction. Additionally, we proposed a frequency-domain alignment loss (FAL) to enable the neural networks to learn frequency-domain information across different augmented samples. It leverages the inherent patterns present in frequency-domain representations to guide the network in capturing and aligning features across diverse augmentation variations, thereby enhancing the model's robustness for the inputting variations. We conduct our experiments on three benchmark datasets, which include MRI (ACDC) for cardiac, CT (Synapse) for abdomen organs, and ultrasound image (BUSI) for breast lesion segmentation. The experimental results demonstrate that our method outperforms state-of-the-art semi-supervised approaches regarding the Dice similaritycoefficient. We find the proposed approach could improve the final performance of the semi-supervised medical image segmentation task. It will help reduce the need for medical image labels. Our code will are available at https://github.com/apple1986/STLFAL.

FAQ: How do I estimate the output gap?

Abstract I investigate the properties of output gaps in New Keynesian dynamic stochastic general equilibrium models and study the relationship between theory-based quantities and the estimates obtained with standard approaches. Theoretical gaps display low-frequency variations, have similar frequency domain representations as potentials and are generally correlated with them. Potentials have important business cycle variability. Existing statistical approaches fail to recognise these features and generate distorted estimates. Gaps are best estimated with a polynomial filter. Explanations for the outcomes are given. I propose a statistical procedure reducing estimation biases.

Structural and sequential regularities modulate phrase-rate neural tracking

Electrophysiological brain activity has been shown to synchronize with the quasi-regular repetition of grammatical phrases in connected speech—so-called phrase-rate neural tracking. Current debate centers around whether this phenomenon is best explained in terms of the syntactic properties of phrases or in terms of syntax-external information, such as the sequential repetition of parts of speech. As these two factors were confounded in previous studies, much of the literature is compatible with both accounts. Here, we used electroencephalography (EEG) to determine if and when the brain is sensitive to both types of information. Twenty native speakers of Mandarin Chinese listened to isochronously presented streams of monosyllabic words, which contained either grammatical two-word phrases (e.g., catch fish, sell house) or non-grammatical word combinations (e.g., full lend, bread far). Within the grammatical conditions, we varied two structural factors: the position of the head of each phrase and the type of attachment. Within the non-grammatical conditions, we varied the consistency with which parts of speech were repeated. Tracking was quantified through evoked power and inter-trial phase coherence, both derived from the frequency-domain representation of EEG responses. As expected, neural tracking at the phrase rate was stronger in grammatical sequences than in non-grammatical sequences without syntactic structure. Moreover, it was modulated by both attachment type and head position, revealing the structure-sensitivity of phrase-rate tracking. We additionally found that the brain tracks the repetition of parts of speech in non-grammatical sequences. These data provide an integrative perspective on the current debate about neural tracking effects, revealing that the brain utilizes regularities computed over multiple levels of linguistic representation in guiding rhythmic computation.

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.

On dynamic fundamental diagrams: Implications for automated vehicles

The traffic fundamental diagram (FD) describes the relationships among fundamental traffic variables of flow, density, and speed. FD represents fundamental properties of traffic streams, giving insights into traffic performance. This paper presents a theoretical investigation of dynamic FD properties, derived directly from vehicle car-following (control) models to model traffic hysteresis. Analytical derivation of dynamic FD is enabled by (i) frequency-domain representation of vehicle kinematics (acceleration, speed, and position) to derive vehicle trajectories based on transfer function and (ii) continuum approximation of density and flow, measured along the derived trajectories using Edie's generalized definitions. The formulation is generic: the derivation of dynamic FD is possible with any analytical car-following (control) laws for human-driven vehicles or automated vehicles (AVs). Numerical experiments shed light on the effects of the density-flow measurement region and car-following parameters on the dynamic FD properties for an AV platoon.

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.