Classical Frequency Research Articles

Functional connectivity across the lifespan: a cross-sectional analysis of changes.

In the era of functional brain networks, our understanding of how they evolve across life in a healthy population remains limited. Here, we investigate functional connectivity across the human lifespan using magnetoencephalography in a cohort of 792 healthy individuals, categorized into young (13 to 30 yr), middle (31 to 54 yr), and late adulthood (55 to 80 yr). Employing corrected imaginary phase-locking value, we map the evolving landscapes of connectivity within delta, theta, alpha, beta, and gamma classical frequency bands among brain areas. Our findings reveal significant shifts in functional connectivity patterns across all frequency bands, with certain networks exhibiting increased connectivity and others decreased, dependent on the frequency band and specific age groups, showcasing the dynamic reorganization of neural networks as age increases. This detailed exploration provides, to our knowledge, the first all-encompassing view of how electrophysiological functional connectivity evolves at different life stages, offering new insights into the brain's adaptability and the intricate interplay of cognitive aging and network connectivity. This work not only contributes to the body of knowledge on cognitive aging and neurological health but also emphasizes the need for further research to develop targeted interventions for maintaining cognitive function in the aging population.

Classical and quantum frequency combs for satellite-based clock synchronization

The next generation of space-based networks for communications, sensing, and navigation will contain optical clocks embedded within satellites. To fully realize the capabilities of such clocks, high-precision clock synchronization across the networks will be necessary. Current experiments have shown the potential for classical frequency combs to synchronize remote optical clocks over free space. However, these classical combs are restricted in precision to the standard quantum limit. Quantum frequency combs, however, which exhibit quantum properties such as squeezing and entanglement, provide pathways for going beyond the standard quantum limit. Here, we present our perspective on the prospects for practical clock synchronization in space using both classical and quantum frequency combs. We detail the current outcomes achievable with a classical frequency comb approach to synchronization, before quantifying the potential outcomes offered by quantum frequency combs. Challenges to be overcome in deploying frequency combs in space are presented, and the implications of almost-perfect synchronization for future space-based applications and experiments are discussed.

Multimodel regional frequency analysis of CMIP extreme precipitation

Abstract A recurrent question in climate risk analysis is determining how climate change will affect
heavy precipitation patterns.
Dividing the globe into homogeneous sub-regions should improve the modeling of heavy precipitation by inferring common regional distributional parameters.
In addition, biases due to model errors in global climate models (GCMs) should be considered to understand the climate response to diffrent forcing effects.
Within this context, we propose an efficient clustering algorithm that, compared to classical regional frequency analysis (RFA) techniques, is covariate-free and accounts for dependence.
It is based on a new non-parametric dissimilarity that combines both the RFA constraint and the pairwise dependence.
We derive asymptotic properties of our dissimilarity estimator, and we interpret it for generalized extreme value distributed pairs.

As an application, we cluster annual daily precipitation maxima of 16 GCMs from the coupled model intercomparison project.
We combine the climatologically consistent subregions identified for all GCMs.
This improves the spatial clusters coherence and outperforms methods either based on margins or on dependence.
Finally, by comparing the natural forcings partition with the one with all forcings, we assess the impact of anthropogenic forcing on precipitation extreme patterns.

Depth range extended digital holography for precise 3D profile imaging via dual frequency interval sweeping

A 3D profile imaging method is proposed by using digital holography swept at dual frequency intervals. The dual frequency interval sweeping is achieved by altering the frequency of the tunable laser with two selected frequency intervals. An infrared camera was used to capture the interferometric patterns during two sweeping periods, and depth profile was reconstructed from multiple digital holograms. Phase image across the target region is extracted at each frequency and the phase at each pixel is varied as the frequencies are swept at a prefixed interval in each period. From measured phases, the congruence equations are constructed to achieve the 3D profile of the target object. The proposed sweeping method extends the measurement range by about ten times compared to the classical single frequency interval sweeping method, with a high depth accuracy of within 20 μm over a range of 4 cm. The proposed method is verified by both numerical simulation and experiment. Automatic extraction of reconstructed distances is achieved to facilitate automated 3D profile imaging.

Perturbation Transmit Beamformer Based Fast Constant Modulus MIMO Radar Waveform Design

In this paper, a fast method to generate a constant-modulus (CM) waveform for a multiple-input, multiple-output, (MIMO) radar is proposed. To simplify the optimization process, the design of the transmit waveform is decoupled from the design of transmit beamformers (TBs) and subpulses. To further improve the computational efficiency, the TBs’ optimization is conducted in parallel, and a linear programming model is proposed to match the desired beampattern. Additionally, we incorporate the perturbation vectors into the TBs’ optimization so that the TBs can be adjusted to satisfy the CM constraint. To quickly generate the CM subpulses with the desired range-compression (RC) performance, the classical linear frequency modulation (LFM) signal and non-LFM (NLFM) are adopted as subpulses. Meanwhile, to guarantee the RC performance of the final angular waveform, the selection of LFM signal parameters is analyzed to achieve a low cross-correlation between subpulses. Numerical simulations verify the transmit beampattern performance, RC performance, and computational efficiency of the proposed method.

When Maturation is Not Linear: Brain Oscillatory Activity in the Process of Aging as Measured by Electrophysiology.

Changes in brain oscillatory activity are commonly used as biomarkers both in cognitive neuroscience and in neuropsychiatric conditions. However, little is known about how its profile changes across maturation. Here we use regression models to characterize magnetoencephalography power changes within classical frequency bands in a sample of 792 healthy participants, covering the range 13 to 80 years old. Our findings unveil complex, non-linear power trajectories that defy the traditional linear paradigm, with notable cortical region variations. Interestingly, slow wave activity increases correlate with improved cognitive performance throughout life and larger gray matter volume in the elderly. Conversely, fast wave activity diminishes in adulthood. Elevated low-frequency activity during aging, traditionally seen as compensatory, may also signify neural deterioration. This dual interpretation, highlighted by our study, reveals the intricate dynamics between brain oscillations, cognitive performance, and aging. It advances our understanding of neurodevelopment and aging by emphasizing the regional specificity and complexity of brain rhythm changes, with implications for cognitive and structural integrity.

Incorporating historical flood events in type-based statistics

Flood statistics form the basis of many hydrologic designs. However, short observation periods can lead to a high degree of uncertainty in the quantile estimates, especially for extreme floods. One way to expand the information used in the statistics and, in particular, to include other exceptional floods in the sample is to take historical floods into account. The use of these floods, which are usually reconstructed from chronicles or flood marks, has long been established for classic flood frequency analysis. However, the fact that historical floods can also have different origins and are therefore not statistically identically distributed has so far been ignored. To avoid this violation of the statistical assumptions, we show how historical floods, subdivided according to their genesis, can be taken into account in type-based flood statistics. For this purpose, the classical partial probability weighted moment (PPWM) method is extended for the type-based mixture model of partial duration series (TMPS). The result is compared to a Markov chain Monte Carlo method in order to compare the differences between the two methods. Type-based statistics can also be used to attribute the different influences of historical floods on the quantile estimate. An example shows that floods associated with long-lasting precipitation in particular are overestimated in short samples, while heavy rainfall floods are comparatively well represented. The results show that the consideration of historical events in type-based statistics not only allows a more balanced view of extreme floods, but also enables the influences of these to be attributed.

High-resolution frequency domain decomposition for modal analysis of bridges using train-induced free-vibrations

Modal parameters are structural inherent characteristics that can be applied for revealing performance of railway bridges. Free vibration signals generated by a passage of train are commonly utilized to estimate the modal parameters of railway bridges due to their higher signal-to-noise ratios compared to random vibrations caused by ambient loads. However, since free vibration signals rapidly decay over time, the available free-vibration data is typically short-time. When using the fast Fourier transform-based spectral estimation method for modal identification from short-time vibration data, a phenomenon known as spectral leakage occurs, leading to miss-identification of some structural modes. In this study, the classical frequency domain decomposition (FDD) is improved for modal identification of railway bridges, in which the higher resolution auto-power spectral density (PSD) and cross-PSD functions are calculated through the autoregressive (AR) model-based method. The AR model-based method improves both the smoothness and resolution of the PSD functions compared to the fast Fourier transform technique. These AR model-based PSD functions are then employed in the FDD process to facilitate frequency and mode shape identification while avoiding spurious noise modes. The proposed eigenvalue fitting technique is subsequently utilized to estimate damping ratios. Numerical simulation data as well as vibration data from an actual bridge are analyzed to validate the proposed method, with a comparison made to the Welch’s PSD-based method. The results demonstrate that the modified FDD approach enables more effective identification of structural modes, even in the presence of closely-spaced modes.

Altered trends of local brain function in classical trigeminal neuralgia patients after a single trigger pain.

To investigate the altered trends of regional homogeneity (ReHo) based on time and frequency, and clarify the time-frequency characteristics of ReHo in 48 classical trigeminal neuralgia (CTN) patients after a single pain stimulate. All patients underwent three times resting-state functional MRI (before stimulation (baseline), after stimulation within 5s (triggering-5s), and in the 30th min of stimulation (triggering-30min)). The spontaneous brain activity was investigated by static ReHo (sReHo) in five different frequency bands and dynamic ReHo (dReHo) methods. In the five frequency bands, the number of brain regions which the sReHo value changed in classical frequency band were most, followed by slow 4 frequency band. The left superior occipital gyrus was only found in slow 2 frequency band and the left superior parietal gyrus was only found in slow 3 frequency band. The dReHo values were changed in midbrain, left thalamus, right putamen, and anterior cingulate cortex, which were all different from the brain regions that the sReHo value altered. There were four altered trends of the sReHo and dReHo, which dominated by decreased at triggering-5s and increased at triggering-30min. The duration of brain function changed was more than 30min after a single pain stimulate, although the pain of CTN was transient. The localized functional homogeneity has time-frequency characteristic in CTN patients after a single pain stimulate, and the changed brain regions of the sReHo in five frequency bands and dReHo complemented to each other. Which provided a certain theoretical basis for exploring the pathophysiology of CTN.

Measurement of the Mapping between Intracranial EEG and fMRI Recordings in the Human Brain.

There are considerable gaps in our understanding of the relationship between human brain activity measured at different temporal and spatial scales. Here, electrocorticography (ECoG) measures were used to predict functional MRI changes in the sensorimotor cortex in two brain states: at rest and during motor performance. The specificity of this relationship to spatial co-localisation of the two signals was also investigated. We acquired simultaneous ECoG-fMRI in the sensorimotor cortex of three patients with epilepsy. During motor activity, high gamma power was the only frequency band where the electrophysiological response was co-localised with fMRI measures across all subjects. The best model of fMRI changes across states was its principal components, a parsimonious description of the entire ECoG spectrogram. This model performed much better than any others that were based either on the classical frequency bands or on summary measures of cross-spectral changes. The region-specific fMRI signal is reflected in spatially and spectrally distributed EEG activity.

Phonological syllables allow children with developmental dyslexia to access words.

Learning to read is a middle-distance race for children worldwide. Most of them succeed in this acquisition with "normal" difficulties that ensue from the progressive (re)structuring of the phonological and orthographic systems. Evidence accumulated on reading difficulties in children with developmental dyslexia (DYS children, henceforth) shows a pervasive phonological deficit. However, the phonological deficit may not be due to degraded phonological representations but rather due to impaired access to them. This study focused on how and to what extent phonological syllables, which are essential reading units in French, were accessible to DYS children to segment and access words. We tested the assumption that DYS children did not strictly have pervasive degraded phonological representations but also have impaired access to phonological and orthographic representations. We administered a visually adapted word-spotting paradigm, engaging both sublexical processing and lexical access, with French native-speaking DYS children (N = 25; Mage in months = 121.6, SD = 3.0) compared with chronological age-matched peers (N = 25; Mage in months = 121.8, SD = 2.7; CA peers henceforth) and reading level-matched peers (N = 25; Mage in months = 94.0, SD = 4.6; RL peers henceforth). Although DYS children were slower and less accurate than CA and RL peers, we found that they used phonological syllables to access and segment words. However, they exhibit neither the classical inhibitory syllable frequency effect nor the lexical frequency effect, which is generally observed in typically developing children. Surprisingly, DYS children did not show strictly degraded phonological representations because they demonstrated phonological syllable-based segmentation abilities, particularly with high-frequency syllables. Their difficulties are rather interpreted in terms of impaired access to orthographic and phonological representations, which could be a direct effect of difficulties in generalizing and consolidating low-frequency syllables. We discuss these results regarding reading acquisition and the specificities of the French linguistic system.

Integrated Sensing and Communication With Delay Alignment Modulation: Performance Analysis and Beamforming Optimization

Delay alignment modulation (DAM) has been recently proposed to enable manipulable channel delay spread for efficient single- or multi-carrier communications. In particular, with perfect delay alignment, inter-symbol interference (ISI) can be eliminated even with single-carrier (SC) transmission, without relying on sophisticated channel equalization. The key ideas of DAM are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay pre-compensation</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path-based beamforming</i> , so that all multi-path signal components may arrive at the receiver simultaneously and be superimposed constructively, rather than causing the detrimental ISI. Compared to the classic orthogonal frequency division multiplexing (OFDM) transmission, DAM-enabled SC communication has several appealing advantages, including low peak-to-average-power ratio (PAPR) and high tolerance for Doppler frequency shift, which renders DAM also appealing for radar sensing. Therefore, in this paper, DAM is investigated for integrated sensing and communication (ISAC) systems. We first study the output signal-to-noise ratios (SNRs) for ISI-free SC communication and radar sensing, respectively, and then derive the closed-form expressions for DAM-based sensing in terms of the ambiguity function (AF) and integrated sidelobe ratio (ISR). Furthermore, we study the beamforming design problem for DAM-based ISAC to maximize the communication SNR while guaranteeing the sensing performance in terms of the sensing SNR and ISR. Finally, we provide performance comparison between DAM and OFDM for ISAC, and it is revealed that DAM signal may achieve better communication and sensing performance, thanks to its low PAPR, reduced guard interval overhead, as well as higher tolerance for Doppler frequency shift. Simulation results are provided to show the great potential of DAM for ISAC.

Comparing feature selection methods to improve the classification of Mild Cognitive Impairment patients based on Magnetoencephalography data

AbstractBackgroundMachine learning (ML) algorithms are generating great interest for early diagnose of Alzheimer’s disease (AD). Despite several approaches have been developed, limited research has been conducted on the impact of feature selection in classification performance. In this study we compare two feature selection methods, LASSO and Elastic Nets (EN), applied to ML algorithms based on magnetoencephalography (MEG) data from mild cognitive impairment (MCI) patients.MethodAn eyes‐closed resting‐state MEG recording was performed by 262 participants (117 healthy controls and 145 MCI). Functional connectivity measures were estimated for all classical frequency bands using the Phase‐Locking Value. To develop the ML algorithms, specific regions of interest from the default mode network, based on the Automatic Anatomical Labelling atlas, were selected, resulting in a total of 325 features. After dividing the dataset into training (80%) and test (20%) sets, feature selection with 10000 iterations and five‐fold cross validation was performed independently for each band using LASSO and EN algorithms. Afterwards, several classification models were trained with a five‐fold cross validation and then validated on the test set, over 500 iterations.ResultThe classifier showing the best performance was the linear Support Vector Machine for the beta frequency band (12‐30 Hz). Given the similarity of the training and test performance values, the results reveal that overfitting was avoided when using the 45 features selected by LASSO instead of the 47 features selected by EN, reaching a validation accuracy of 77%. Additionally, LASSO consistently identified three functional connectivity links as relevant in all frequency bands but alpha: right superior frontal gyrus &amp; right superior frontal gyrus orbital, left posterior cingulate cortex &amp; left hippocampus, right posterior cingulate cortex &amp; right precuneus.ConclusionML algorithms applied to MEG data can successfully discriminate MCI patients from healthy controls. In addition, LASSO algorithm applied for feature selection leads to better classification performance. Moreover, the resulting relevant functional connectivity links involve areas affected by AD pathology even in early stages of its development (López‐Sanz et al., 2019). Further exploration of this methodology is needed, combining this data with structural neuroimaging or complementary biomarkers.

Altered brain function in classical trigeminal neuralgia patients: ALFF, ReHo, and DC static- and dynamic-frequency study.

The present study aimed to clarify the brain function of classical trigeminal neuralgia (CTN) by analyzing 77 CTN patients and age- and gender-matched 73 healthy controls (HCs) based on three frequency bands of the static and dynamic amplitude of low-frequency fluctuation, regional homogeneity, and degree centrality (sALFF, sReHo, sDC, dALFF, dReHo, and dDC). Compared to HCs, the number of altered brain regions was different in three frequency bands, and the classical frequency band was most followed by slow-4 in CTN patients. Cerrelellum_8_L (sReHo), Cerrelellum_8_R (sDC), Calcarine_R (sDC), and Caudate_R (sDC) were found only in classical frequency band, while Precuneus_L (sALFF) and Frontal_Inf_Tri_L (sReHo) were found only in slow-4 frequency band. Except for the above six brain regions, the others overlapped in the classical and slow-4 frequency bands. CTN seriously affects the mental health of patients, and some different brain regions are correlated with clinical parameters. The static and dynamic indicators of brain function were complementary in CTN patients, and the changing brain regions showed frequency specificity. Compared to slow-5 frequency band, slow-4 is more consistent with the classical frequency band, which could be valuable in exploring the pathophysiology of CTN.

The testing of a multivariate probabilistic framework for reservoir safety evaluation and flood risks assessment in Slovakia: A study on the Parná and Belá Rivers

Abstract Intense floods represent a challenge to risk management. While they are multivariate in their nature, they are often studied in practice from univariate perspectives. Classical frequency analyses, which establish a relation between the peak flow or volume and the frequency of exceedance, may lead to improper risk estimations and mitigations. Therefore, it is necessary to study floods as multivariate stochastic events having mutually correlated characteristics, such as peak flood flow, corresponding volume and duration. The joint distribution properties of these characteristics play an important role in the assessment of flood risk and reservoir safety evaluation. In addition, the study of flood hydrographs is useful because of the inherent dependencies among their practice-relevant characteristics present on-site and in the regional records. This study aims to provide risk analysts with a consistent multivariate probabilistic framework using a copula-based approach. The framework respects and describes the dependence structures among the flood peaks, volumes, and durations of observed and synthetic control flood hydrographs. The seasonality of flood generation is respected by separate analyses of floods in the summer and winter seasons. A control flood hydrograph is understood as a theoretical/synthetic discharge hydrograph, which is determined by the flood peak with the chosen probability of exceedance, the corresponding volume, and the time duration with the corresponding probability. The framework comprises five steps: 1. Separation of the observed hydrographs, 2. Analysis of the flood characteristics and their dependence, 3. Modelling the marginal distributions, 4. A copula-based approach for modelling joint distributions of the flood peaks, volumes and durations, 5. Construction of synthetic flood hydrographs. The flood risk assessment and reservoir safety evaluation are described by hydrograph analyses and the conditional joint probabilities of the exceedance of the flood volume and duration conditioned on flood peak. The proposed multivariate probabilistic framework was tested and demonstrated based on data from two contrasting catchments in Slovakia. Based on the findings, the study affirms that the trivariate copula-based approach is a practical option for assessing flood risks and for reservoir safety.

Acoustic signatures of porous rocks permeated by partially saturated, aligned planar fractures

AbstractThe presence of sets of vertical, parallel fractures is very common in the Earth's upper crust. Notably, open fractures exert critical control on the mechanical and hydraulic properties of the host formation. There is great interest in understanding how fractures interact with seismic waves, as this knowledge could be used to detect and characterize fractures from seismic data. When a seismic wave travels through a fractured formation, it induces oscillatory fluid pressure diffusion between the fractures and the embedding porous background, a physical process that produces attenuation and dispersion of the seismic wave. Although there are numerous studies on this topic, the case of parallel fractures saturated with different immiscible fluids, such as brine and CO2, remains rather unexplored. With these motivations, in this work, we propose an analytical approach to compute the phase velocity and attenuation of P‐waves travelling perpendicularly to a set of planar, parallel fractures. While we consider that the background is saturated with brine, the fractures can be saturated with brine or gas. Our numerical analysis shows for the first time that two manifestations of fluid pressure diffusion arise in these cases. One of them, associated with relatively high levels of attenuation, is due to fluid pressure diffusion occurring between consecutive fractures saturated with different fluids. In this case, the fluid pressure diffusion process is initiated at a fracture saturated with brine and reaches a consecutive fracture saturated with gas. The other fluid pressure diffusion manifestation, on the other hand, arises at higher frequencies, is characterized by lower levels of attenuation and results from the interaction in the background of fluid pressure diffusion processes initiated at consecutive fractures, irrespective of the fluid content. Finally, by considering a stochastic distribution of the two fluids and a classical frequency of interest in seismic experiments, we obtain P‐wave attenuation and phase velocity as functions of the fracture gas saturation. This approach could be of interest for the remote detection and quantification of pore fluids using seismic waves.

Increasing mustard (Brassica juncea L.) yields through exposure sound and preventive pest management based on refugia plants

Abstract. In Indonesia, mustard plants will increase by 8.2% in 2021, but more than that is needed to meet the community's needs due to a growing population. Pests and fertilization problems hinder expected growth. The provision of plant fertilizers can be replaced through the application of sound. Exposure sounds to plants can increase plant growth by opening stomata, improving water absorption, and increasing plant nutrient uptake. This study aimed to examine the application of sound effects and refugia plants t890po increase the growth and yield of mustard greens (Brassica juncea L.). The study used a Time's Series Randomized Block Design with 3 replications. The first factor is sound applications (S) consisting of S0 = without sound, S1 = rock music (Frequency 21-14,000 Hz), and S2 = classical sound (Frequency 21-14,000 Hz). The second factor is the refugia plant (R) consisting of R0 = without refugia, R1 = Tagetes erecta L., R2 = Zinnia elegans L, and R3 = Ocimum bassilicum L. The application of classical sound frequency (20-14,000 Hz) affects the growth process of mustard plants through the increase in plant height (14.5%), leaf area (20.92%), wet weight (3.5%), dry weight (26.41%), total chlorophyll (11.62%) and plant N content (31.03%). Meanwhile, rock music frequency (20-14,000 Hz) can increase plant height (2.97%), leaf area (19.11%), and total stomata (9.6%). Refugia plants affect the process of plant protection through their ability to attract pests in the research area.

Experimental investigation of transonic buffeting, frequency lock-in and their dependence on structural characteristics

Transonic buffet is a phenomenon that appears in compressible flow around an airfoil and plays a substantial role in the limitation of the flight envelope of commercial aircraft. If the structural natural frequencies of the wing are similar to the buffet frequency, the oscillation of the compression shock, fluid, and structure may interact (transonic buffeting) and lead to strong loads and potential structural failure. Numerical research has shown that structural parameters can have a significant effect on the onset point of shock oscillations as well as on the typology of the fluid–structure interaction, which presented classical structural excitation, modal veering, or frequency lock-in.The aim of this research is a systematic experimental investigation to examine the structural effects and the lock-in phenomenon. It provides a partial validation of the numerical results available in the literature. A lightweight, elastically-suspended wing model (OAT15A profile) was tested in the Trisonic Wind Tunnel Munich. Optical measurement techniques were deployed to non-intrusively observe the flow-induced density gradient field (background-oriented Schlieren) and the structural deformation and displacement of the wing (digital image correlation). Mass ratios varied from 282 to 322 and the half-chord-based, reduced natural pitch frequency ranged from 0.169 to 0.280. The experimental results confirm the existence of frequency lock-in, an interaction dominated by the structural mode that presents high but limited pitch amplitudes for natural pitch frequencies above the natural buffet frequency. The effects of mass ratio and natural pitch frequency on the interaction are discussed. A substantial effect of the mass ratio on the onset of buffeting and the resulting pitch amplitude for frequency lock-in was discovered.

State estimation of the dynamic behavior of plasma properties in a Hall effect thruster discharge

The dynamic behaviors of the plasma properties in a Hall effect thruster discharge channel are estimated using a physics-constrained extended Kalman filter (PC-EKF) with a zero-dimensional global plasma model. The state estimates obtained using the global plasma EKF model are augmented by experimental data, in this case a discharge current signal. The use of state estimation allows for the determination of time-resolved plasma behaviors that may be difficult to measure experimentally, such as electron temperature and bulk velocity. The model is applied to investigate the plasma behavior at various thruster operating conditions, i.e. at varying discharge voltages and discharge currents. The estimated plasma properties are used to determine the classical electron collision frequency and the anomalous electron scattering frequency, which are shown to vary in time.

A fully asymptotic preserving decomposed multi-group method for the frequency-dependent radiative transfer equations

The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion equations are two simplified models that can approximate the solution to FRTE in the thick opacity regime. The frequency discretization for the two limit models highly affects the numerical accuracy. However, classical frequency discretization for FRTE considers only the absorbing coefficient. In this paper, we propose a new decomposed multi-group method for frequency discretization that is not only AP in both gray radiation diffusion and frequency-dependent diffusion limits, but also the frequency discretization of the limiting models can be tuned. Based on the decomposed multi-group method, a full AP scheme in frequency, time, and space is proposed. Several numerical examples are used to verify the performance of the proposed scheme.