By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional...By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation（FrST） which satisfies additivity.By virtue of the integration technique within the ordered product of operators（IWOP） we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa＋a/2 and exp[iα/2（a^2 ＋a^＋2）.The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.展开更多
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing...Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.展开更多
Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalizat...Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.展开更多
We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transfo...We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.展开更多
Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed int...With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ 1+μ 2, whereμ 1 is a bounded measure on 0<=s<=2 andμ 2 is slowly increasing measure on (sχC|Re(s)=1)}展开更多
This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to c...This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).展开更多
Objective:The present study investigated the cytoprotective effects of a Pogonatherum paniceum extract prepared with 80%ethanol(PPE)using synchrotron radiation-based Fourier transform infrared(SR-FTIR)microspectroscop...Objective:The present study investigated the cytoprotective effects of a Pogonatherum paniceum extract prepared with 80%ethanol(PPE)using synchrotron radiation-based Fourier transform infrared(SR-FTIR)microspectroscopy and determined its phytochemical profile.Methods:The volatile and polyphenolic compounds in PPE were characterized using gas chromatography–mass spectrometry and liquid chromatography–mass spectrometry,respectively.The antioxidant capacity of PPE was evaluated using chemical and cell-based assays.The SR-FTIR microspectroscopy was performed to evaluate the cytoprotective effect of PPE by identifying changes in macromolecule composition in tert-butyl hydroperoxide(t BuOOH)-induced oxidative damage in RAW264.7 cells.Results:A total of 48 volatile compounds and 28 polyphenol components were found in PPE.PPE exhibited a high potential for antioxidant activity by scavenging the intracellular reactive oxygen species in t Bu OOH-induced oxidative damage in RAW264.7 cells.PPE treatment also significantly protected RAW264.7 cells against t BuOOH-induced toxicity and restored cell viability.The SR-FTIR analysis revealed that t BuOOH increased the lipid and ester lipid content in RAW264.7 cells.The PPE exerted a cytoprotective effect by decreasing the levels of lipid and ester lipid compounds that had been elevated by t BuOOH in RAW264.7 cells.These findings indicate that PPE has cytoprotective potential due to its ability to inhibit endogenous reactive oxygen species.Conclusion:This study extends the current knowledge on the phytochemistry of PPE and its antioxidant and cytoprotective effects.These findings support the use of SR-FTIR microspectroscopy to determine the cytoprotective effects of natural products.PPE extract may be a candidate compound for new therapeutics and nutraceuticals that target the prevention of oxidative stress-associated diseases.展开更多
The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transf...The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.展开更多
The internal microstructures of rock materials, including mineral heterogeneity and intrinsic microdefects, exert a significant influence on their nonlinear mechanical and cracking behaviors. It is of great significan...The internal microstructures of rock materials, including mineral heterogeneity and intrinsic microdefects, exert a significant influence on their nonlinear mechanical and cracking behaviors. It is of great significance to accurately characterize the actual microstructures and their influence on stress and damage evolution inside the rocks. In this study, an image-based fast Fourier transform (FFT) method is developed for reconstructing the actual rock microstructures by combining it with the digital image processing (DIP) technique. A series of experimental investigations were conducted to acquire information regarding the actual microstructure and the mechanical properties. Based on these experimental evidences, the processed microstructure information, in conjunction with the proposed micromechanical model, is incorporated into the numerical calculation. The proposed image-based FFT method was firstly validated through uniaxial compression tests. Subsequently, it was employed to predict and analyze the influence of microstructure on macroscopic mechanical behaviors, local stress distribution and the internal crack evolution process in brittle rocks. The distribution of feldspar is considerably more heterogeneous and scattered than that of quartz, which results in a greater propensity for the formation of cracks in feldspar. It is observed that initial cracks and new cracks, including intragranular and boundary ones, ultimately coalesce and connect as the primary through cracks, which are predominantly distributed along the boundary of the feldspar. This phenomenon is also predicted by the proposed numerical method. The results indicate that the proposed numerical method provides an effective approach for analyzing, understanding and predicting the nonlinear mechanical and cracking behaviors of brittle rocks by taking into account the actual microstructure characteristics.展开更多
The capacity to diagnose faults in rolling bearings is of significant practical importance to ensure the normal operation of the equipment.Frequency-domain features can effectively enhance the identification of fault ...The capacity to diagnose faults in rolling bearings is of significant practical importance to ensure the normal operation of the equipment.Frequency-domain features can effectively enhance the identification of fault modes.However,existing methods often suffer from insufficient frequency-domain representation in practical applications,which greatly affects diagnostic performance.Therefore,this paper proposes a rolling bearing fault diagnosismethod based on aMulti-Scale FusionNetwork(MSFN)using the Time-Division Fourier Transform(TDFT).The method constructs multi-scale channels to extract time-domain and frequency-domain features of the signal in parallel.A multi-level,multi-scale filter-based approach is designed to extract frequency-domain features in a segmented manner.A cross-attention mechanism is introduced to facilitate the fusion of the extracted time-frequency domain features.The performance of the proposed method is validated using the CWRU and Ottawa datasets.The results show that the average accuracy of MSFN under complex noisy signals is 97.75%and 94.41%.The average accuracy under variable load conditions is 98.68%.This demonstrates its significant application potential compared to existing methods.展开更多
The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for ...The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.展开更多
Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband ...Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband or detail value characteristics under healthy and various faulty operating conditions. The most reliable phase current among the three phase currents was selected using an approach that employs the fuzzy entropy measure. Data were trained with a neural network system, and the fault detection algorithm was verified using the unknown data. Results of the proposed approach based on Fourier and wavelet transformations indicate that the faults can be properly classified into six categories. The training error is 5.3×10-7, and the average test error is 0.103.展开更多
In this paper,we propose a hybrid forecasting model(HFM)for the short-term electric load forecasting using artificial neural network(ANN),discrete Fourier transformation(DFT)and principal component analysis(PCA)techni...In this paper,we propose a hybrid forecasting model(HFM)for the short-term electric load forecasting using artificial neural network(ANN),discrete Fourier transformation(DFT)and principal component analysis(PCA)techniques in order to attain higher prediction accuracy.Firstly,we estimate Fourier coefficients by the DFT for predicting the next-day load curve with an ANN and obtain approximate load curves by applying the inverse discrete Fourier transformation.Approximate curves,together with other input variables,are given to the ANN to predict the next-day hourly load curves.Furthermore,we predict PCA scores to obtain approximate load curves in the first step,which are then given to the ANN again in the second step.Both DFT and PCA models use input variables such as calendrical and meteorological data as well as past electric loads.Applying those models for forecasting hourly electric load in the metropolitan area of Japan for January and May in 2018,we train our models using historical data since January 2008.The forecast results show that the HFM consisting of“ANN with DFT”and“ANN with PCA”predicts next-day hourly loads more accurately than the conventional three-layered ANN approach.Their corresponding mean average absolute errors show 2.7%for ANN with DFT,2.6%for ANN with PCA and 3.0%for the conventional ANN approach.We also find that in May,when electric demand is smaller with smaller fluctuations,forecasting errors are much smaller than January for all the models.Thus,we can conclude that the HFM would contribute to attaining significantly higher forecasting accuracy.展开更多
By a quantum mechanical analysis of the additive rule Fa [Fβ[f]] = Fα＋β[f], which the fractional Fourier transformation （FrFT） Fα [f] should satisfy, we reveal that the position-momentum mutual- transformation ...By a quantum mechanical analysis of the additive rule Fa [Fβ[f]] = Fα＋β[f], which the fractional Fourier transformation （FrFT） Fα [f] should satisfy, we reveal that the position-momentum mutual- transformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation （CFrFT）, which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.展开更多
Electromagnetic Spectrum(EMS)recognition is vital in spectrum control,interference location,electronic countermeasures,etc.However,samples of high-value targets are incredibly scarce,even single,and are easily overwhe...Electromagnetic Spectrum(EMS)recognition is vital in spectrum control,interference location,electronic countermeasures,etc.However,samples of high-value targets are incredibly scarce,even single,and are easily overwhelmed by noise and numerous low-value targets,resulting in poor recognition accuracy using traditional methods.Furthermore,the great similarity between samples from the same manufacturer,model,and batch,makes Specific Emitter Identification(SEI)with the EMS especially challenging.Based on the powerful extension and extraction ability of the Fractional Fourier Transform(FrFT)for detailed features,this paper proposes a novel algorithm for the EMS recognition under a single-sample condition.The proposed method constructs a feature matrix FrFT-M from the results of the FrFT under specific orders for each sample.Then,the most relevant item,obtained by analyzing the correlations among FrFT-Ms between the unidentified sample and known samples,determines the optimal recognition.Three simple tests are conducted,including two simulations considering fifteen basic waveforms and six typical radar signals,and one experiment using STM32 microcontroller boards.The detection results of simulated and experimental data show that the accuracies of all three cases are higher than 86%,even for samples of the same model.Our method is promising and may have significant value in other fields.展开更多
Deepfake-generated fake faces,commonly utilized in identity-related activities such as political propaganda,celebrity impersonations,evidence forgery,and familiar fraud,pose new societal threats.Although current deepf...Deepfake-generated fake faces,commonly utilized in identity-related activities such as political propaganda,celebrity impersonations,evidence forgery,and familiar fraud,pose new societal threats.Although current deepfake generators strive for high realism in visual effects,they do not replicate biometric signals indicative of cardiac activity.Addressing this gap,many researchers have developed detection methods focusing on biometric characteristics.These methods utilize classification networks to analyze both temporal and spectral domain features of the remote photoplethysmography(rPPG)signal,resulting in high detection accuracy.However,in the spectral analysis,existing approaches often only consider the power spectral density and neglect the amplitude spectrum—both crucial for assessing cardiac activity.We introduce a novel method that extracts rPPG signals from multiple regions of interest through remote photoplethysmography and processes them using Fast Fourier Transform(FFT).The resultant time-frequency domain signal samples are organized into matrices to create Matrix Visualization Heatmaps(MVHM),which are then utilized to train an image classification network.Additionally,we explored various combinations of time-frequency domain representations of rPPG signals and the impact of attention mechanisms.Our experimental results show that our algorithm achieves a remarkable detection accuracy of 99.22%in identifying fake videos,significantly outperforming mainstream algorithms and demonstrating the effectiveness of Fourier Transform and attention mechanisms in detecting fake faces.展开更多
Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of pre...Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of precision spectroscopy and trace gas detection.Here,we report the development of a mid-infrared Fourier transform spectrometer based on an optical frequency comb combined with a Herriott-type multipass cell.Using this instrument,the broadband absorption spectra of several important molecules,including methane,acetylene,water molecules and nitrous oxide,are measured by near real-time data acquisition in the 2800-3500 cm^(-1)spectral region.The achieved minimum detectable absorption of the instrument is 4.4×10^(-8)cm^(-1)·Hz^(-1/2)per spectral element.Broadband spectra of H_(2)0 are fited using the Voigt profile multispectral fitting technique and the consistency of the concentration inversion is 1%.Our system also enables precise spectroscopic measurements,and it allows the determination of the spectral line positions and upper state constants of N_(2)O in the(0002)-(1000)band,with results in good agreement with those reported by Toth[Appl.Opt.30,5289(1991)].展开更多
Using the Weyl quantization scheme and based on the Fourier slice transformation （FST） of the Wigner operator, we construct a new expansion formula of the density operator p, with the expansion coefficient being the...Using the Weyl quantization scheme and based on the Fourier slice transformation （FST） of the Wigner operator, we construct a new expansion formula of the density operator p, with the expansion coefficient being the FST of p＇s classical Weyl correspondence, and the latter the Fourier transformation of p＇s quantum tomogram. The coordinate momentum intermediate representation is used as the Radon transformation of the Wigner operator.展开更多
Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employ...Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11304126)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130532)+2 种基金the Natural Science Fund for Colleges and Universities in Jiangsu Province,China(Grant No.13KJB140003)the Postdoctoral Science Foundation of China(Grant No.2013M541608)the Postdoctoral Science Foundation of Jiangsu Province,China(Grant No.1202012B)
文摘By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation（FrST） which satisfies additivity.By virtue of the integration technique within the ordered product of operators（IWOP） we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa＋a/2 and exp[iα/2（a^2 ＋a^＋2）.The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
文摘Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.
基金National Natural Science Foundation of China under Grant No.10775097
文摘Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.
基金Project supported by the Specialized Research Fund for Doctoral Program of High Education of Chinathe National Natural Science Foundation of China (Grant Nos. 10874174 and 10947017/A05)
文摘We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.
文摘Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
基金the National Natural Science F oundation of China (198710 65 ) and Hua Cheng Mathematics Science Foundation
文摘With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ 1+μ 2, whereμ 1 is a bounded measure on 0<=s<=2 andμ 2 is slowly increasing measure on (sχC|Re(s)=1)}
文摘This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).
基金supported by the Basic Research Fund from Thailand Science Research and Innovation through Sisaket Rajabhat University(grant number:FF.13/2564)。
文摘Objective:The present study investigated the cytoprotective effects of a Pogonatherum paniceum extract prepared with 80%ethanol(PPE)using synchrotron radiation-based Fourier transform infrared(SR-FTIR)microspectroscopy and determined its phytochemical profile.Methods:The volatile and polyphenolic compounds in PPE were characterized using gas chromatography–mass spectrometry and liquid chromatography–mass spectrometry,respectively.The antioxidant capacity of PPE was evaluated using chemical and cell-based assays.The SR-FTIR microspectroscopy was performed to evaluate the cytoprotective effect of PPE by identifying changes in macromolecule composition in tert-butyl hydroperoxide(t BuOOH)-induced oxidative damage in RAW264.7 cells.Results:A total of 48 volatile compounds and 28 polyphenol components were found in PPE.PPE exhibited a high potential for antioxidant activity by scavenging the intracellular reactive oxygen species in t Bu OOH-induced oxidative damage in RAW264.7 cells.PPE treatment also significantly protected RAW264.7 cells against t BuOOH-induced toxicity and restored cell viability.The SR-FTIR analysis revealed that t BuOOH increased the lipid and ester lipid content in RAW264.7 cells.The PPE exerted a cytoprotective effect by decreasing the levels of lipid and ester lipid compounds that had been elevated by t BuOOH in RAW264.7 cells.These findings indicate that PPE has cytoprotective potential due to its ability to inhibit endogenous reactive oxygen species.Conclusion:This study extends the current knowledge on the phytochemistry of PPE and its antioxidant and cytoprotective effects.These findings support the use of SR-FTIR microspectroscopy to determine the cytoprotective effects of natural products.PPE extract may be a candidate compound for new therapeutics and nutraceuticals that target the prevention of oxidative stress-associated diseases.
基金Supported by National Natural Science Foundation of China(11571089,11501164)Natural Science Founda-tion of Hebei Province(A2019205299)+1 种基金the Foundation of Hebei Education Department(ZD2018065,ZD2019053)Hebei Normal University(L2019Z01).
文摘The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.
基金supported by the National Natural Science Foundation of China(Grant No.11802332)the China Scholarship Council(Grant No.202206435003)the Fundamental Research Funds for the Central Universities(Grant No.2024ZKPYLJ03).
文摘The internal microstructures of rock materials, including mineral heterogeneity and intrinsic microdefects, exert a significant influence on their nonlinear mechanical and cracking behaviors. It is of great significance to accurately characterize the actual microstructures and their influence on stress and damage evolution inside the rocks. In this study, an image-based fast Fourier transform (FFT) method is developed for reconstructing the actual rock microstructures by combining it with the digital image processing (DIP) technique. A series of experimental investigations were conducted to acquire information regarding the actual microstructure and the mechanical properties. Based on these experimental evidences, the processed microstructure information, in conjunction with the proposed micromechanical model, is incorporated into the numerical calculation. The proposed image-based FFT method was firstly validated through uniaxial compression tests. Subsequently, it was employed to predict and analyze the influence of microstructure on macroscopic mechanical behaviors, local stress distribution and the internal crack evolution process in brittle rocks. The distribution of feldspar is considerably more heterogeneous and scattered than that of quartz, which results in a greater propensity for the formation of cracks in feldspar. It is observed that initial cracks and new cracks, including intragranular and boundary ones, ultimately coalesce and connect as the primary through cracks, which are predominantly distributed along the boundary of the feldspar. This phenomenon is also predicted by the proposed numerical method. The results indicate that the proposed numerical method provides an effective approach for analyzing, understanding and predicting the nonlinear mechanical and cracking behaviors of brittle rocks by taking into account the actual microstructure characteristics.
基金fully supported by the Frontier Exploration Projects of Longmen Laboratory(No.LMQYTSKT034)Key Research and Development and Promotion of Special(Science and Technology)Project of Henan Province,China(No.252102210158)。
文摘The capacity to diagnose faults in rolling bearings is of significant practical importance to ensure the normal operation of the equipment.Frequency-domain features can effectively enhance the identification of fault modes.However,existing methods often suffer from insufficient frequency-domain representation in practical applications,which greatly affects diagnostic performance.Therefore,this paper proposes a rolling bearing fault diagnosismethod based on aMulti-Scale FusionNetwork(MSFN)using the Time-Division Fourier Transform(TDFT).The method constructs multi-scale channels to extract time-domain and frequency-domain features of the signal in parallel.A multi-level,multi-scale filter-based approach is designed to extract frequency-domain features in a segmented manner.A cross-attention mechanism is introduced to facilitate the fusion of the extracted time-frequency domain features.The performance of the proposed method is validated using the CWRU and Ottawa datasets.The results show that the average accuracy of MSFN under complex noisy signals is 97.75%and 94.41%.The average accuracy under variable load conditions is 98.68%.This demonstrates its significant application potential compared to existing methods.
文摘The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.
基金Project supported by the Second Stage of Brain Korea 21 Projects
文摘Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband or detail value characteristics under healthy and various faulty operating conditions. The most reliable phase current among the three phase currents was selected using an approach that employs the fuzzy entropy measure. Data were trained with a neural network system, and the fault detection algorithm was verified using the unknown data. Results of the proposed approach based on Fourier and wavelet transformations indicate that the faults can be properly classified into six categories. The training error is 5.3×10-7, and the average test error is 0.103.
文摘In this paper,we propose a hybrid forecasting model(HFM)for the short-term electric load forecasting using artificial neural network(ANN),discrete Fourier transformation(DFT)and principal component analysis(PCA)techniques in order to attain higher prediction accuracy.Firstly,we estimate Fourier coefficients by the DFT for predicting the next-day load curve with an ANN and obtain approximate load curves by applying the inverse discrete Fourier transformation.Approximate curves,together with other input variables,are given to the ANN to predict the next-day hourly load curves.Furthermore,we predict PCA scores to obtain approximate load curves in the first step,which are then given to the ANN again in the second step.Both DFT and PCA models use input variables such as calendrical and meteorological data as well as past electric loads.Applying those models for forecasting hourly electric load in the metropolitan area of Japan for January and May in 2018,we train our models using historical data since January 2008.The forecast results show that the HFM consisting of“ANN with DFT”and“ANN with PCA”predicts next-day hourly loads more accurately than the conventional three-layered ANN approach.Their corresponding mean average absolute errors show 2.7%for ANN with DFT,2.6%for ANN with PCA and 3.0%for the conventional ANN approach.We also find that in May,when electric demand is smaller with smaller fluctuations,forecasting errors are much smaller than January for all the models.Thus,we can conclude that the HFM would contribute to attaining significantly higher forecasting accuracy.
基金The work was supported by the National Natural Science Foundation of China （Grant Nos. 11105133 and 11175113） and the National Basic Research Program of China （973 Program） （Grant No. 2012CB922001）.
文摘By a quantum mechanical analysis of the additive rule Fa [Fβ[f]] = Fα＋β[f], which the fractional Fourier transformation （FrFT） Fα [f] should satisfy, we reveal that the position-momentum mutual- transformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation （CFrFT）, which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.
基金supported in part by the National Natural Science Foundation of China(No.62293495)。
文摘Electromagnetic Spectrum(EMS)recognition is vital in spectrum control,interference location,electronic countermeasures,etc.However,samples of high-value targets are incredibly scarce,even single,and are easily overwhelmed by noise and numerous low-value targets,resulting in poor recognition accuracy using traditional methods.Furthermore,the great similarity between samples from the same manufacturer,model,and batch,makes Specific Emitter Identification(SEI)with the EMS especially challenging.Based on the powerful extension and extraction ability of the Fractional Fourier Transform(FrFT)for detailed features,this paper proposes a novel algorithm for the EMS recognition under a single-sample condition.The proposed method constructs a feature matrix FrFT-M from the results of the FrFT under specific orders for each sample.Then,the most relevant item,obtained by analyzing the correlations among FrFT-Ms between the unidentified sample and known samples,determines the optimal recognition.Three simple tests are conducted,including two simulations considering fifteen basic waveforms and six typical radar signals,and one experiment using STM32 microcontroller boards.The detection results of simulated and experimental data show that the accuracies of all three cases are higher than 86%,even for samples of the same model.Our method is promising and may have significant value in other fields.
基金supported by the National Nature Science Foundation of China(Grant Number:61962010).
文摘Deepfake-generated fake faces,commonly utilized in identity-related activities such as political propaganda,celebrity impersonations,evidence forgery,and familiar fraud,pose new societal threats.Although current deepfake generators strive for high realism in visual effects,they do not replicate biometric signals indicative of cardiac activity.Addressing this gap,many researchers have developed detection methods focusing on biometric characteristics.These methods utilize classification networks to analyze both temporal and spectral domain features of the remote photoplethysmography(rPPG)signal,resulting in high detection accuracy.However,in the spectral analysis,existing approaches often only consider the power spectral density and neglect the amplitude spectrum—both crucial for assessing cardiac activity.We introduce a novel method that extracts rPPG signals from multiple regions of interest through remote photoplethysmography and processes them using Fast Fourier Transform(FFT).The resultant time-frequency domain signal samples are organized into matrices to create Matrix Visualization Heatmaps(MVHM),which are then utilized to train an image classification network.Additionally,we explored various combinations of time-frequency domain representations of rPPG signals and the impact of attention mechanisms.Our experimental results show that our algorithm achieves a remarkable detection accuracy of 99.22%in identifying fake videos,significantly outperforming mainstream algorithms and demonstrating the effectiveness of Fourier Transform and attention mechanisms in detecting fake faces.
基金supported by the National Natural Science Foundation China(No.42022051,No.U21A2028)Youth Innovation Promotion Association of the Chinese Academy of Sciences(No.Y202089)the HFIPS Director's Fund(No.YZJJ202101,No.BJPY2023A02).
文摘Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of precision spectroscopy and trace gas detection.Here,we report the development of a mid-infrared Fourier transform spectrometer based on an optical frequency comb combined with a Herriott-type multipass cell.Using this instrument,the broadband absorption spectra of several important molecules,including methane,acetylene,water molecules and nitrous oxide,are measured by near real-time data acquisition in the 2800-3500 cm^(-1)spectral region.The achieved minimum detectable absorption of the instrument is 4.4×10^(-8)cm^(-1)·Hz^(-1/2)per spectral element.Broadband spectra of H_(2)0 are fited using the Voigt profile multispectral fitting technique and the consistency of the concentration inversion is 1%.Our system also enables precise spectroscopic measurements,and it allows the determination of the spectral line positions and upper state constants of N_(2)O in the(0002)-(1000)band,with results in good agreement with those reported by Toth[Appl.Opt.30,5289(1991)].
基金Project supported by the Natural Science Foundation of Huangshi Institute of Technology,China (Grant No. 10yjz03R)the National Natural Science Foundation of China (Grant No. 10874174)
文摘Using the Weyl quantization scheme and based on the Fourier slice transformation （FST） of the Wigner operator, we construct a new expansion formula of the density operator p, with the expansion coefficient being the FST of p＇s classical Weyl correspondence, and the latter the Fourier transformation of p＇s quantum tomogram. The coordinate momentum intermediate representation is used as the Radon transformation of the Wigner operator.
基金supported by the National Natural Science Foundation of China(61801503).
文摘Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.
