In modern wireless communication and electromagnetic control,automatic modulationclassification(AMC)of orthogonal frequency division multiplexing(OFDM)signals plays animportant role.However,under Doppler frequency shi...In modern wireless communication and electromagnetic control,automatic modulationclassification(AMC)of orthogonal frequency division multiplexing(OFDM)signals plays animportant role.However,under Doppler frequency shift and complex multipath channel conditions,extracting discriminative features from high-order modulation signals and ensuring model inter-pretability remain challenging.To address these issues,this paper proposes a Fourier attention net-work(FAttNet),which combines an attention mechanism with a Fourier analysis network(FAN).Specifically,the method directly converts the input signal to the frequency domain using the FAN,thereby obtaining frequency features that reflect the periodic variations in amplitude and phase.Abuilt-in attention mechanism then automatically calculates the weights for each frequency band,focusing on the most discriminative components.This approach improves both classification accu-racy and model interpretability.Experimental validation was conducted via high-order modulationsimulation using an RF testbed.The results show that under three different Doppler frequencyshifts and complex multipath channel conditions,with a signal-to-noise ratio of 10 dB,the classifi-cation accuracy can reach 89.1%,90.4%and 90%,all of which are superior to the current main-stream methods.The proposed approach offers practical value for dynamic spectrum access and sig-nal security detection,and it makes important theoretical contributions to the application of deeplearning in complex electromagnetic signal recognition.展开更多
Different physical, mechanical and chemical processes, such as： ion implantation, oxidation, nitridation and others create on the surface of materials residual stress state, characterized by high level and strong gra...Different physical, mechanical and chemical processes, such as： ion implantation, oxidation, nitridation and others create on the surface of materials residual stress state, characterized by high level and strong gradient. X-ray diffraction method widely used for stress measurements has some difficulties in interpretation of experimental data, when the depth of X-ray penetration is compared with thickness of surface layer where inhomogeneous stress distribution is localized. Early it has been shown by authors that diffraction line broadening occurs when analyzed surface is characterized by strong gradient. The interest to study the diffraction line broadening is connected to the possibility of obtaining information about parameters of surface stress distribution. In the present paper the convolution and deconvolution concepts of Fourier analysis were applied to study X ray diffraction line broadening caused by surface stress gradients. Developed methodology allows determining of stress distribution in superficial layers of materials.展开更多
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
We report a spatially modulated polarimetry scheme by using a zero-order vortex half-wave retarder(ZVHR)and a spatial Fourier analysis method.A ZVHR is employed to analyze the input polarized light and convert it into...We report a spatially modulated polarimetry scheme by using a zero-order vortex half-wave retarder(ZVHR)and a spatial Fourier analysis method.A ZVHR is employed to analyze the input polarized light and convert it into a vectorial optical field,and an analyzer is set after the ZVHR to form an hourglass intensity pattern due to the spatial polarization modulation.Then,the input light’s Stokes parameters can be calculated by spatial Fourier analysis of the hourglass pattern with a single shot.The working principle of the polarimeter has been analyzed by the Stokes-Mueller formalism,and some quantitative measuring experiments of different polarization states have been demonstrated.The experimental results indicate that the proposed polarimeter is accurate,robust,and simple to use.展开更多
In this paper, Fourier and Wavelet transformation were adopted to analyze shape char- acteristics, with twelve simple shapes and two types of second phases from real microstructure mor- phology. According to the resul...In this paper, Fourier and Wavelet transformation were adopted to analyze shape char- acteristics, with twelve simple shapes and two types of second phases from real microstructure mor- phology. According to the results of Fast Fourier transformation （FFT）, the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors （SSRE） of Wavelet transformation （WT） signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi- larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig- natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.展开更多
This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary ...This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.展开更多
A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is presented. The function of the modified elastic light scattering spectrum is regarded as a function of wave number...A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is presented. The function of the modified elastic light scattering spectrum is regarded as a function of wave number factor, Q=2λ-1sin（θ/2）. The modified spectrum has a constant oscillation period with its frequency proportional to the average diameter of cell nuclei. To the same average diameter, the different relative refractive indexes of epithelial cell nuclei only induce the horizontal shift of the spectra. Both the oscillation frequency and the horizontal shift are quantified by the fast Fourier transform on the modified spectra. The average diameter can be figured out through the peak frequency divided by the value of the refractive index of the surrounding medium. The phase angle of the peak frequency has an approximate linear relationship with the relative refractive index of epithelial cell nuclei.展开更多
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey pa...Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.展开更多
In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without ...In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.展开更多
Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedu...Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion (p< 0.05) for vastus medialis (189.9 ± 82.1 for STFT vs 148.6 ± 60.2 for CWT) and vastus lateralis (151.6 ± 49.6 for STFT vs 103.5 ± 27.9 for CWT). In conclusion, despite the EMG signal did not change (p> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.展开更多
Fast Fourier Transfer Image Processing was widely applied to the analysis of wood anatomy structure in re-cent years. The cells in the wood transverse section have obviously periodicity and regularity. FFT power spect...Fast Fourier Transfer Image Processing was widely applied to the analysis of wood anatomy structure in re-cent years. The cells in the wood transverse section have obviously periodicity and regularity. FFT power spectral patternscan extract the periodic characteristics so that they can be compared. identified and classified quaytitatively. This paperSummarizes the application of FFT image analysis in wood science and the general way to study wood anatomy by FFT.展开更多
Otolith shape is species specific and is an ideal marker of fish population affiliation. In this study, otolith shape of spottedtail goby Synechogobius ommaturus is used to identify stocks in different spawning locati...Otolith shape is species specific and is an ideal marker of fish population affiliation. In this study, otolith shape of spottedtail goby Synechogobius ommaturus is used to identify stocks in different spawning locations in the Yellow Sea. The main objectives of this study are to explore the potential existence of local stocks of spottedtail goby in the Yellow Sea by analysis of otolith shape, and to investigate ambient impacts on otolith shape. Spottedtail goby was sampled in five locations in the Yellow Sea in 2007 and 2008. Otoliths are described using variables correlated to size (otolith area, perimeter, length, width, and weight) and shape (rectangularity, circularity, and 20 Fourier harmonics). Only standardized otolith variables are used so that the effect of otolith size on the shape variables could be eliminated. There is no significant difference among variables of sex, year, and side (left and right). However, the otolith shapes of the spring stocks and the autumn stocks differ significantly. Otolith shape differences are greater among locations than between years. Correct classification rate of spottedtail goby with the otolith shape at different sampling locations range from 29.7%–77.4%.展开更多
A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichu...A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods（Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis）were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s^（-1）. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.展开更多
We tested the use of otolith shape analysis to discriminate between species and stocks of five goby species( Ctenotrypauchen chinensis, Odontamblyopus lacepedii, Amblychaeturichthys hexanema, Chaeturichthys stigmatias...We tested the use of otolith shape analysis to discriminate between species and stocks of five goby species( Ctenotrypauchen chinensis, Odontamblyopus lacepedii, Amblychaeturichthys hexanema, Chaeturichthys stigmatias, and Acanthogobius hasta) found in northern Chinese coastal waters. The five species were well differentiated with high overall classification success using shape indices(83.7%), elliptic Fourier coefficients(98.6%), or the combination of both methods(94.9%). However, shape analysis alone was only moderately successful at discriminating among the four stocks(Liaodong Bay, LD; Bohai Bay, BH; Huanghe(Yellow) River estuary HRE, and Jiaozhou Bay, JZ stocks) of A. hasta(50%–54%) and C. stigmatias(65.7%–75.8%). For these two species, shape analysis was moderately successful at discriminating the HRE or JZ stocks from other stocks, but failed to effectively identify the LD and BH stocks. A large number of otoliths were misclassified between the HRE and JZ stocks, which are geographically well separated. The classification success for stock discrimination was higher using elliptic Fourier coefficients alone(70.2%) or in combination with shape indices(75.8%) than using only shape indices(65.7%) in C. stigmatias whereas there was little difference among the three methods for A. hasta. Our results supported the common belief that otolith shape analysis is generally more effective for interspecific identification than intraspecific discrimination. Moreover, compared with shape indices analysis, Fourier analysis improves classification success during inter- and intra-species discrimination by otolith shape analysis, although this did not necessarily always occur in all fish species.展开更多
This work aims to contribute to the characterization and understanding ofinfragravity waves on two beaches with erosion problems. For this reason, we have used an array of ADCP and a pressure sensor to measure wave pa...This work aims to contribute to the characterization and understanding ofinfragravity waves on two beaches with erosion problems. For this reason, we have used an array of ADCP and a pressure sensor to measure wave parameters and pressure inside and outside of the surf zone during the dry and rainy period in the beaches of Galerazamba and Manzanillo del Mar （both dissipative and eroded beaches） located in the Colombian Caribbean coast. Based on these measurements, we have carried out a spectral analysis in order to identify the frequency components that characterize the wave and its energy; thus, we identified the characteristic frequencies of iufragravity waves to finally filter the infragravity signal on each beach in different seasonal periods. Among the results of the Welch spectrum applied to surface elevation time series, we found that, the frequencies＇ energy of the sea-swell band decreases due to bottom friction and wave breaking as the wave approaches the shore, while the frequencies＇ energy of the infragravity band increases significantly. In addition, for the wavelet analysis, we could observe how the energy of the infragravity band, especially the lowest frequencies gain energy as the waves approaches the coast. Furthermore, based on the infragravity wave obtained from the extreme wave event registered during the field campaign we can conclude that the contribution of this signal is important in the erosion problems presented in the beaches of Galerazamba and Manzanillo del Mar. Finally, these results show the need to realize other studies that allow us to understand deeply, the role of infragravity waves on the morphological changes that occurs in these beaches.展开更多
Sagittal otoliths morphology were compared to identify five Pampus species of the Chinese coast（Chinese pomfret Pampus chinensis, grey pomfret P. cinereus, southern lesser pomfret P. minor, plumage pomfret P.punctati...Sagittal otoliths morphology were compared to identify five Pampus species of the Chinese coast（Chinese pomfret Pampus chinensis, grey pomfret P. cinereus, southern lesser pomfret P. minor, plumage pomfret P.punctatissmus, and Pampus sp.）. Otoliths demonstrated species-specific characteristics with noticeable differences in overall shape, margin and anterior region among species. With species divergence, otoliths get thinner following further developed rostrum and anti-rostrum. Interspecies variation in otolith could associate with experienced different temperature and water column. The discriminant analysis presented a high classification accuracy of 96.6%, which confirms the inter-specific distinction of otolith shape and enable the species identification.展开更多
It is well known that Fourier analysis or wavelet analysis is a very powerful and useful tool for a function since they convert time-domain problems into frequency-domain problems. Are there similar tools for a matrix...It is well known that Fourier analysis or wavelet analysis is a very powerful and useful tool for a function since they convert time-domain problems into frequency-domain problems. Are there similar tools for a matrix？ By pairing a matrix to a piecewise function,a Haar-like wavelet is used to set up a similar tool for matrix analyzing, resulting in new methods for matrix approximation and orthogonal decomposition. By using our method, one can approximate a matrix by matrices with different orders. Our method also results in a new matrix orthogonal decomposition, reproducing Haar transformation for matrices with orders of powers of two. The computational complexity of the new orthogonal decomposition is linear. That is, for an m × n matrix, the computational complexity is O（mn）. In addition,when the method is applied to k-means clustering, one can obtain that k-means clustering can be equivalently converted to the problem of finding a best approximation solution of a function. In fact, the results in this paper could be applied to any matrix related problems.In addition, one can also employ other wavelet transformations and Fourier transformation to obtain similar results.展开更多
In this study,reclaimed asphalt pavement(RAP)used in different percentages in hot mix asphalt(HMA)and warm mix asphalt(WMA)were tested for moisture,fracture and rutting resistance adding hydrogenated castor oil flakes...In this study,reclaimed asphalt pavement(RAP)used in different percentages in hot mix asphalt(HMA)and warm mix asphalt(WMA)were tested for moisture,fracture and rutting resistance adding hydrogenated castor oil flakes(HCOF)as rejuvenating agent.Volumetric and Marshall parameters were evaluated for both types of mixtures.Addition of 5%of HCOF by weight of binder content in RAP found to restore properties of aged binder.WMA mix was made by adding 0.1%Zycotherm by weight of optimum binder content.Moisture,rutting and fracture damage performance were assessed utilizing indirect tensile strength,wheel tracking and semi-circular bending tests.The mix's tensile strength ratio increased by 2.3%in the HMA with RAP(HMA-R)mix compared to the WMA with RAP(WMA-R)mix at 10%RAP content.HMA mixes provide better resistance to rutting compared to WMA.However,40%of RAP content HMA-R and WMA-R using HCOF rejuvenator shows greater rutting performance compared to other RAP mix.HMA-R mix fracture resistance increased by 18.14%compared to WMA-R mix when RAP content increases to 40%.Regression analyses were carried out to validate the strain energy found from fracture damage analysis of both HMA-R and WMA-R with R2 value more than 0.9.HMA-R protected moisture and fracture damage better than WMA-R.The rejuvenating efficiency of HCOF was further validated using Fourier transform infrared and microscopic analysis.展开更多
To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ens...To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ensemble empirical mode decomposition(EEMD)and cross-correlation algorithm was proposed.Firstly,a fast Fourier transform(FFT)spectrum analysis was utilized to ascertain the frequency range of the signal.Secondly,data acquisition was conducted at an appropriate sampling frequency,and the acquired Doppler flow rate signal was then decomposed into a series of intrinsic mode functions(IMFs)by EEMD.Subsequently,these decomposed IMFs were recombined based on their energy entropy,and then the noise of the recombined Doppler flow rate signal was removed by cross-correlation filtering.Finally,an ideal ultrasonic Doppler flow rate signal was extracted.Simulation and experimental verification show that the proposed Doppler flow signal processing method can effectively enhance the signal-to-noise ratio(SNR)and extend the lower limit of measurement of the ultrasonic Doppler flow meter.展开更多
In this paper, Wavelet Analysis Method (WAM) is introduced to analyse the non-stationary, shock signals. The theory and construction method of wavelet, the fast algorithms of wavelet analysis are presented. As an exam...In this paper, Wavelet Analysis Method (WAM) is introduced to analyse the non-stationary, shock signals. The theory and construction method of wavelet, the fast algorithms of wavelet analysis are presented. As an example, the gear testing signal has been analysed by WAM, and the results of WAM are compared with that of Fourier spectrum. The advantages of WAM are clearly shown.展开更多
基金supported by the National Natural Science Foundation of China(No.62027801).
文摘In modern wireless communication and electromagnetic control,automatic modulationclassification(AMC)of orthogonal frequency division multiplexing(OFDM)signals plays animportant role.However,under Doppler frequency shift and complex multipath channel conditions,extracting discriminative features from high-order modulation signals and ensuring model inter-pretability remain challenging.To address these issues,this paper proposes a Fourier attention net-work(FAttNet),which combines an attention mechanism with a Fourier analysis network(FAN).Specifically,the method directly converts the input signal to the frequency domain using the FAN,thereby obtaining frequency features that reflect the periodic variations in amplitude and phase.Abuilt-in attention mechanism then automatically calculates the weights for each frequency band,focusing on the most discriminative components.This approach improves both classification accu-racy and model interpretability.Experimental validation was conducted via high-order modulationsimulation using an RF testbed.The results show that under three different Doppler frequencyshifts and complex multipath channel conditions,with a signal-to-noise ratio of 10 dB,the classifi-cation accuracy can reach 89.1%,90.4%and 90%,all of which are superior to the current main-stream methods.The proposed approach offers practical value for dynamic spectrum access and sig-nal security detection,and it makes important theoretical contributions to the application of deeplearning in complex electromagnetic signal recognition.
文摘Different physical, mechanical and chemical processes, such as： ion implantation, oxidation, nitridation and others create on the surface of materials residual stress state, characterized by high level and strong gradient. X-ray diffraction method widely used for stress measurements has some difficulties in interpretation of experimental data, when the depth of X-ray penetration is compared with thickness of surface layer where inhomogeneous stress distribution is localized. Early it has been shown by authors that diffraction line broadening occurs when analyzed surface is characterized by strong gradient. The interest to study the diffraction line broadening is connected to the possibility of obtaining information about parameters of surface stress distribution. In the present paper the convolution and deconvolution concepts of Fourier analysis were applied to study X ray diffraction line broadening caused by surface stress gradients. Developed methodology allows determining of stress distribution in superficial layers of materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(NSFC)(No.61975235)the Natural Science Foundation of Hunan Province(No.2019JJ40342)。
文摘We report a spatially modulated polarimetry scheme by using a zero-order vortex half-wave retarder(ZVHR)and a spatial Fourier analysis method.A ZVHR is employed to analyze the input polarized light and convert it into a vectorial optical field,and an analyzer is set after the ZVHR to form an hourglass intensity pattern due to the spatial polarization modulation.Then,the input light’s Stokes parameters can be calculated by spatial Fourier analysis of the hourglass pattern with a single shot.The working principle of the polarimeter has been analyzed by the Stokes-Mueller formalism,and some quantitative measuring experiments of different polarization states have been demonstrated.The experimental results indicate that the proposed polarimeter is accurate,robust,and simple to use.
基金the support received from the National Natural Science Foundation of China (No.51275414)the Aeronautical Science Foundation of China (No.2011ZE53059)
文摘In this paper, Fourier and Wavelet transformation were adopted to analyze shape char- acteristics, with twelve simple shapes and two types of second phases from real microstructure mor- phology. According to the results of Fast Fourier transformation （FFT）, the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors （SSRE） of Wavelet transformation （WT） signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi- larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig- natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.
基金supported by the NSFC grant 11801143J.Lu’s research is partially supported by the NSFC grant 11901213+3 种基金the National Key Research and Development Program of China grant 2021YFA1002900supported by the NSFC grant 11801140,12171177the Young Elite Scientists Sponsorship Program by Henan Association for Science and Technology of China grant 2022HYTP0009the Program for Young Key Teacher of Henan Province of China grant 2021GGJS067.
文摘This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.
基金supported by the National Natural Science Foundation of China(Nos.10904072 and 10704039)the Startup Foundation(No.AB411994)the Development Foundation from Nanjing University of Science and Technology(No.XKF09043).
文摘A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is presented. The function of the modified elastic light scattering spectrum is regarded as a function of wave number factor, Q=2λ-1sin（θ/2）. The modified spectrum has a constant oscillation period with its frequency proportional to the average diameter of cell nuclei. To the same average diameter, the different relative refractive indexes of epithelial cell nuclei only induce the horizontal shift of the spectra. Both the oscillation frequency and the horizontal shift are quantified by the fast Fourier transform on the modified spectra. The average diameter can be figured out through the peak frequency divided by the value of the refractive index of the surrounding medium. The phase angle of the peak frequency has an approximate linear relationship with the relative refractive index of epithelial cell nuclei.
文摘Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
文摘In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.
文摘Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion (p< 0.05) for vastus medialis (189.9 ± 82.1 for STFT vs 148.6 ± 60.2 for CWT) and vastus lateralis (151.6 ± 49.6 for STFT vs 103.5 ± 27.9 for CWT). In conclusion, despite the EMG signal did not change (p> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.
文摘Fast Fourier Transfer Image Processing was widely applied to the analysis of wood anatomy structure in re-cent years. The cells in the wood transverse section have obviously periodicity and regularity. FFT power spectral patternscan extract the periodic characteristics so that they can be compared. identified and classified quaytitatively. This paperSummarizes the application of FFT image analysis in wood science and the general way to study wood anatomy by FFT.
基金Supported by the National Basic Research Program of China (973 program) (No.2005CB422306)the National Natural Science Foundation of China under the Science Fund for Creative Research Groups (No.40821004)the Natural Science Foundation of Shandong Province (No.Y2008D21)
文摘Otolith shape is species specific and is an ideal marker of fish population affiliation. In this study, otolith shape of spottedtail goby Synechogobius ommaturus is used to identify stocks in different spawning locations in the Yellow Sea. The main objectives of this study are to explore the potential existence of local stocks of spottedtail goby in the Yellow Sea by analysis of otolith shape, and to investigate ambient impacts on otolith shape. Spottedtail goby was sampled in five locations in the Yellow Sea in 2007 and 2008. Otoliths are described using variables correlated to size (otolith area, perimeter, length, width, and weight) and shape (rectangularity, circularity, and 20 Fourier harmonics). Only standardized otolith variables are used so that the effect of otolith size on the shape variables could be eliminated. There is no significant difference among variables of sex, year, and side (left and right). However, the otolith shapes of the spring stocks and the autumn stocks differ significantly. Otolith shape differences are greater among locations than between years. Correct classification rate of spottedtail goby with the otolith shape at different sampling locations range from 29.7%–77.4%.
基金supported by Study on Key Techniques of convective gale monitoring and forecasting in spring in Southern China (GYHY201406002)the National Natural Science Foundation of China (41705027,41775140,41175060,91437215,and 41575047)+1 种基金the research project of Heavy Rain and Drought-Flood Disasters in Plateau and Basin Key Laboratory of Sichuan Province (SZKT2016002)Open projects of Plateau Atmosphere and Environment Key Laboratory of Sichuan Province (PAEKL-2015-K2)
文摘A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods（Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis）were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s^（-1）. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.
基金Supported by the National Natural Science Foundation of China(NSFC)(Nos.40976084,U1406403,41121064)
文摘We tested the use of otolith shape analysis to discriminate between species and stocks of five goby species( Ctenotrypauchen chinensis, Odontamblyopus lacepedii, Amblychaeturichthys hexanema, Chaeturichthys stigmatias, and Acanthogobius hasta) found in northern Chinese coastal waters. The five species were well differentiated with high overall classification success using shape indices(83.7%), elliptic Fourier coefficients(98.6%), or the combination of both methods(94.9%). However, shape analysis alone was only moderately successful at discriminating among the four stocks(Liaodong Bay, LD; Bohai Bay, BH; Huanghe(Yellow) River estuary HRE, and Jiaozhou Bay, JZ stocks) of A. hasta(50%–54%) and C. stigmatias(65.7%–75.8%). For these two species, shape analysis was moderately successful at discriminating the HRE or JZ stocks from other stocks, but failed to effectively identify the LD and BH stocks. A large number of otoliths were misclassified between the HRE and JZ stocks, which are geographically well separated. The classification success for stock discrimination was higher using elliptic Fourier coefficients alone(70.2%) or in combination with shape indices(75.8%) than using only shape indices(65.7%) in C. stigmatias whereas there was little difference among the three methods for A. hasta. Our results supported the common belief that otolith shape analysis is generally more effective for interspecific identification than intraspecific discrimination. Moreover, compared with shape indices analysis, Fourier analysis improves classification success during inter- and intra-species discrimination by otolith shape analysis, although this did not necessarily always occur in all fish species.
基金The Program of Administrative Department of Science,Technology and Innovation under contract No.COLCIENCIAS 03932013
文摘This work aims to contribute to the characterization and understanding ofinfragravity waves on two beaches with erosion problems. For this reason, we have used an array of ADCP and a pressure sensor to measure wave parameters and pressure inside and outside of the surf zone during the dry and rainy period in the beaches of Galerazamba and Manzanillo del Mar （both dissipative and eroded beaches） located in the Colombian Caribbean coast. Based on these measurements, we have carried out a spectral analysis in order to identify the frequency components that characterize the wave and its energy; thus, we identified the characteristic frequencies of iufragravity waves to finally filter the infragravity signal on each beach in different seasonal periods. Among the results of the Welch spectrum applied to surface elevation time series, we found that, the frequencies＇ energy of the sea-swell band decreases due to bottom friction and wave breaking as the wave approaches the shore, while the frequencies＇ energy of the infragravity band increases significantly. In addition, for the wavelet analysis, we could observe how the energy of the infragravity band, especially the lowest frequencies gain energy as the waves approaches the coast. Furthermore, based on the infragravity wave obtained from the extreme wave event registered during the field campaign we can conclude that the contribution of this signal is important in the erosion problems presented in the beaches of Galerazamba and Manzanillo del Mar. Finally, these results show the need to realize other studies that allow us to understand deeply, the role of infragravity waves on the morphological changes that occurs in these beaches.
基金The Public Science and Technology Research Funds Projects of Ocean under contract No.201305030the Specialized Research Fund for the Doctoral Program of Higher Education under contract No.20120132130001the Fundamental Research Funds for the Central Universities under contract No.201262004
文摘Sagittal otoliths morphology were compared to identify five Pampus species of the Chinese coast（Chinese pomfret Pampus chinensis, grey pomfret P. cinereus, southern lesser pomfret P. minor, plumage pomfret P.punctatissmus, and Pampus sp.）. Otoliths demonstrated species-specific characteristics with noticeable differences in overall shape, margin and anterior region among species. With species divergence, otoliths get thinner following further developed rostrum and anti-rostrum. Interspecies variation in otolith could associate with experienced different temperature and water column. The discriminant analysis presented a high classification accuracy of 96.6%, which confirms the inter-specific distinction of otolith shape and enable the species identification.
文摘It is well known that Fourier analysis or wavelet analysis is a very powerful and useful tool for a function since they convert time-domain problems into frequency-domain problems. Are there similar tools for a matrix？ By pairing a matrix to a piecewise function,a Haar-like wavelet is used to set up a similar tool for matrix analyzing, resulting in new methods for matrix approximation and orthogonal decomposition. By using our method, one can approximate a matrix by matrices with different orders. Our method also results in a new matrix orthogonal decomposition, reproducing Haar transformation for matrices with orders of powers of two. The computational complexity of the new orthogonal decomposition is linear. That is, for an m × n matrix, the computational complexity is O（mn）. In addition,when the method is applied to k-means clustering, one can obtain that k-means clustering can be equivalently converted to the problem of finding a best approximation solution of a function. In fact, the results in this paper could be applied to any matrix related problems.In addition, one can also employ other wavelet transformations and Fourier transformation to obtain similar results.
文摘In this study,reclaimed asphalt pavement(RAP)used in different percentages in hot mix asphalt(HMA)and warm mix asphalt(WMA)were tested for moisture,fracture and rutting resistance adding hydrogenated castor oil flakes(HCOF)as rejuvenating agent.Volumetric and Marshall parameters were evaluated for both types of mixtures.Addition of 5%of HCOF by weight of binder content in RAP found to restore properties of aged binder.WMA mix was made by adding 0.1%Zycotherm by weight of optimum binder content.Moisture,rutting and fracture damage performance were assessed utilizing indirect tensile strength,wheel tracking and semi-circular bending tests.The mix's tensile strength ratio increased by 2.3%in the HMA with RAP(HMA-R)mix compared to the WMA with RAP(WMA-R)mix at 10%RAP content.HMA mixes provide better resistance to rutting compared to WMA.However,40%of RAP content HMA-R and WMA-R using HCOF rejuvenator shows greater rutting performance compared to other RAP mix.HMA-R mix fracture resistance increased by 18.14%compared to WMA-R mix when RAP content increases to 40%.Regression analyses were carried out to validate the strain energy found from fracture damage analysis of both HMA-R and WMA-R with R2 value more than 0.9.HMA-R protected moisture and fracture damage better than WMA-R.The rejuvenating efficiency of HCOF was further validated using Fourier transform infrared and microscopic analysis.
基金supported by National Natural Science Foundation of China(No.61973234)Tianjin Science and Technology Plan Project(No.22YDTPJC00090)。
文摘To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ensemble empirical mode decomposition(EEMD)and cross-correlation algorithm was proposed.Firstly,a fast Fourier transform(FFT)spectrum analysis was utilized to ascertain the frequency range of the signal.Secondly,data acquisition was conducted at an appropriate sampling frequency,and the acquired Doppler flow rate signal was then decomposed into a series of intrinsic mode functions(IMFs)by EEMD.Subsequently,these decomposed IMFs were recombined based on their energy entropy,and then the noise of the recombined Doppler flow rate signal was removed by cross-correlation filtering.Finally,an ideal ultrasonic Doppler flow rate signal was extracted.Simulation and experimental verification show that the proposed Doppler flow signal processing method can effectively enhance the signal-to-noise ratio(SNR)and extend the lower limit of measurement of the ultrasonic Doppler flow meter.
文摘In this paper, Wavelet Analysis Method (WAM) is introduced to analyse the non-stationary, shock signals. The theory and construction method of wavelet, the fast algorithms of wavelet analysis are presented. As an example, the gear testing signal has been analysed by WAM, and the results of WAM are compared with that of Fourier spectrum. The advantages of WAM are clearly shown.
