Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology refe...Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology referred to as doubly multiple parameters weighted fractional Fourier transform(DMWFRFT), which can strengthen the physical layer security of wireless communication. This paper introduces the concept of DM-WFRFT based on multiple parameters WFRFT(MP-WFRFT), and then presents its four properties. Based on these properties, the parameters decryption probability is analyzed in terms of the number of parameters. The number of parameters for DM-WFRFT is more than that of the MP-WFRFT,which indicates that the proposed scheme can further strengthen the the physical layer security. Lastly, some numerical simulations are carried out to illustrate that the efficiency of proposed DM-WFRFT is related to preventing eavesdropping, and the effect of parameters variety on the system performance is associated with the bit error ratio(BER).展开更多
In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechani...In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.展开更多
Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is diffic...Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner Ville distribution （SPWD） were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.展开更多
Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-compone...Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.展开更多
Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional p...Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.展开更多
The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function...The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J /E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb /N 0(when estimation difference is 90% between trans- mitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference un-der Pb=10-2.展开更多
In this paper a joint timing and frequency synchronization method based on Fractional Fourier Transform （FIFT） is proposed for Orthogonal Frequency-Division Multiplexing （OFDM） system. The combination of two chirp...In this paper a joint timing and frequency synchronization method based on Fractional Fourier Transform （FIFT） is proposed for Orthogonal Frequency-Division Multiplexing （OFDM） system. The combination of two chirp signals with opposite chirp rates are used as the training signal, the received training signal with timing and frequency offset is transformed by FrFT and the two peaks representing two chirps in FrFT domain are detected, then the position coordinates of the two peaks are precisely corrected and substituted into an equation group to calculate timing and frequency offset simultaneously. This method only needs one FrFT calculation to implement synchronization, the computational complexity is equal to that of FFT and less than that of correlation or maximum likelihood calculation of existing methods, and estimation range of frequency offset is Large, greater than half the signal bandwidth, while the simulation results show that even at low SNR it can accurately estimate timing and frequency offset and the estimation error is less than that of existing methods.展开更多
Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original...Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed technique is robust to lossy compression attack.展开更多
In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertain...In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.展开更多
Sampling is a bridge between continuous-time and discrete-time signals,which is import-ant to digital signal processing.The fractional Fourier transform(FrFT)that serves as a generaliz-ation of the FT can characterize...Sampling is a bridge between continuous-time and discrete-time signals,which is import-ant to digital signal processing.The fractional Fourier transform(FrFT)that serves as a generaliz-ation of the FT can characterize signals in multiple fractional Fourier domains,and therefore can provide new perspectives for signal sampling and reconstruction.In this paper,we review recent de-velopments of the sampling theorem associated with the FrFT,including signal reconstruction and fractional spectral analysis of uniform sampling,nonuniform samplings due to various factors,and sub-Nyquist sampling,where bandlimited signals in the fractional Fourier domain are mainly taken into consideration.Moreover,we provide several future research topics of the sampling theorem as-sociated with the FrFT.展开更多
Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributio...Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.展开更多
By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalu...By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.展开更多
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 diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified imag...Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.展开更多
A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the rec...A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and bit-error-ratio (BER) are obtained.展开更多
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields.The fractional Fourier transform （FRFT） is applied to treat the propagation of Lorentz beams.Based on the de...This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields.The fractional Fourier transform （FRFT） is applied to treat the propagation of Lorentz beams.Based on the definition of convolution and the convolution theorem of the Fourier transform,an analytical expression for a Lorentz beam passing through a FRFT system has been derived.By using the derived formula,the properties of a Lorentz beam in the FRFT plane are illustrated numerically.展开更多
Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order ...Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order to overcome the shortcomings,the STFrFT method with adaptive window function is proposed.In this method,the window function of STFrFT is ad-aptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion,so as to obtain a time-frequency distribution that better matches the desired signal.This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window func-tion,improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated sig-nals.展开更多
With the vigorous development of national infrastructure construction and public information construction,video surveillance systems have gradually penetrated various fields.The current key frame extraction technology...With the vigorous development of national infrastructure construction and public information construction,video surveillance systems have gradually penetrated various fields.The current key frame extraction technology has inadequate target details and inaccurate judgment of local actions.Addressing this problem,a key frame extraction method based on fractional Fourier transform is proposed.This method obtained the phase spectra information of different orders by performing fractional Fourier transform on the surveillance video frames.Next,the method designed an adaptive algorithm based on the golden section point to select the transformation order.Then,the phase spectrum information of two adjacent frames was used to characterize the changes in the global and local motion states of the target.The final step was to extract key frames based on this.Experimental results show that,compared with the previous methods,the key frames extracted by the method proposed in this paper can correctly capture the changes in the global and local motion states of the target.展开更多
To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) mo...To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) module is proposed. In the proposed scheme, the original signal is first decomposed into eight sub-signals and then merged into three component signals by the same carrier pattern. The three signals have mathematical constraint relations among themselves that can counteract the channel fading. They are simultaneously transmitted via three independent antennas after delay regulating. At the receiver, an inverse 8-WFRFT module is employed to obtain the estimated original signal by processing the received signal. Then, the bit error rate(BER) performance, transmitting power, transmission rate, power spectrum and computational complexity of the proposed scheme are analysed in detail. Numerical results show that the proposed scheme has a superior performance compared to STBC based three-antenna transmission scheme, in terms of BER performance.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
文摘Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology referred to as doubly multiple parameters weighted fractional Fourier transform(DMWFRFT), which can strengthen the physical layer security of wireless communication. This paper introduces the concept of DM-WFRFT based on multiple parameters WFRFT(MP-WFRFT), and then presents its four properties. Based on these properties, the parameters decryption probability is analyzed in terms of the number of parameters. The number of parameters for DM-WFRFT is more than that of the MP-WFRFT,which indicates that the proposed scheme can further strengthen the the physical layer security. Lastly, some numerical simulations are carried out to illustrate that the efficiency of proposed DM-WFRFT is related to preventing eavesdropping, and the effect of parameters variety on the system performance is associated with the bit error ratio(BER).
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents at the College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.
基金supported by National Natural Science Foundation of China(Grant No.40874059)
文摘Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner Ville distribution （SPWD） were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.
基金Sponsored by the National Natural Science Foundation of China (60232010 ,60572094)the National Science Foundation of China for Distin-guished Young Scholars (60625104)
文摘Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.
基金supported by the National Natural Science Foundation of China (606720846060203760736006)
文摘Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.
基金Supported by Fund of National Key Lab.of Communication.
文摘The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J /E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb /N 0(when estimation difference is 90% between trans- mitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference un-der Pb=10-2.
文摘In this paper a joint timing and frequency synchronization method based on Fractional Fourier Transform （FIFT） is proposed for Orthogonal Frequency-Division Multiplexing （OFDM） system. The combination of two chirp signals with opposite chirp rates are used as the training signal, the received training signal with timing and frequency offset is transformed by FrFT and the two peaks representing two chirps in FrFT domain are detected, then the position coordinates of the two peaks are precisely corrected and substituted into an equation group to calculate timing and frequency offset simultaneously. This method only needs one FrFT calculation to implement synchronization, the computational complexity is equal to that of FFT and less than that of correlation or maximum likelihood calculation of existing methods, and estimation range of frequency offset is Large, greater than half the signal bandwidth, while the simulation results show that even at low SNR it can accurately estimate timing and frequency offset and the estimation error is less than that of existing methods.
文摘Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed technique is robust to lossy compression attack.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60473141)the Natural Science Foundation of Liaoning Province of China (Grant No. 20062191)
文摘In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.
基金supported in part by the National Natural Foundation of China(NSFC)(Nos.62027801 and U1833203)the Beijing Natural Science Foundation(No.L191004).
文摘Sampling is a bridge between continuous-time and discrete-time signals,which is import-ant to digital signal processing.The fractional Fourier transform(FrFT)that serves as a generaliz-ation of the FT can characterize signals in multiple fractional Fourier domains,and therefore can provide new perspectives for signal sampling and reconstruction.In this paper,we review recent de-velopments of the sampling theorem associated with the FrFT,including signal reconstruction and fractional spectral analysis of uniform sampling,nonuniform samplings due to various factors,and sub-Nyquist sampling,where bandlimited signals in the fractional Fourier domain are mainly taken into consideration.Moreover,we provide several future research topics of the sampling theorem as-sociated with the FrFT.
基金This work was supported by the National Natural Science Foundation of China(91538201)the Taishan Scholar Project of Shandong Province(ts201511020)the project supported by Chinese National Key Laboratory of Science and Technology on Information System Security(6142111190404).
文摘Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.
文摘By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.
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 diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.
文摘A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and bit-error-ratio (BER) are obtained.
基金Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department of China
文摘This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields.The fractional Fourier transform （FRFT） is applied to treat the propagation of Lorentz beams.Based on the definition of convolution and the convolution theorem of the Fourier transform,an analytical expression for a Lorentz beam passing through a FRFT system has been derived.By using the derived formula,the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
基金supported by the National Natural Science Found-ation of China(No.61571454)Special Fund for Taishan Scholar Project(No.201712072)。
文摘Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order to overcome the shortcomings,the STFrFT method with adaptive window function is proposed.In this method,the window function of STFrFT is ad-aptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion,so as to obtain a time-frequency distribution that better matches the desired signal.This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window func-tion,improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated sig-nals.
基金supported by the National Natural Science Foundation of China(Nos.61702347,62027801 and 61972267)Natural Science Fund of Hebei Province(No.F2017210161),and Hebei Province Graduate Student Innovation Ability Training Funding Project.
文摘With the vigorous development of national infrastructure construction and public information construction,video surveillance systems have gradually penetrated various fields.The current key frame extraction technology has inadequate target details and inaccurate judgment of local actions.Addressing this problem,a key frame extraction method based on fractional Fourier transform is proposed.This method obtained the phase spectra information of different orders by performing fractional Fourier transform on the surveillance video frames.Next,the method designed an adaptive algorithm based on the golden section point to select the transformation order.Then,the phase spectrum information of two adjacent frames was used to characterize the changes in the global and local motion states of the target.The final step was to extract key frames based on this.Experimental results show that,compared with the previous methods,the key frames extracted by the method proposed in this paper can correctly capture the changes in the global and local motion states of the target.
基金supported by the National Basic Research Program of China (2013CB329003)the National Natural Science Foundation Program of China (No. 61671179)Funds for Science and Technology on Information Transmission and Dissemination in Communication Networks Laboratory (EX156410046)
文摘To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) module is proposed. In the proposed scheme, the original signal is first decomposed into eight sub-signals and then merged into three component signals by the same carrier pattern. The three signals have mathematical constraint relations among themselves that can counteract the channel fading. They are simultaneously transmitted via three independent antennas after delay regulating. At the receiver, an inverse 8-WFRFT module is employed to obtain the estimated original signal by processing the received signal. Then, the bit error rate(BER) performance, transmitting power, transmission rate, power spectrum and computational complexity of the proposed scheme are analysed in detail. Numerical results show that the proposed scheme has a superior performance compared to STBC based three-antenna transmission scheme, in terms of BER performance.
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.
