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
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L^2(R) instead of Hermite-Gaussian functions. The new orthonormal basis is gained ...This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L^2(R) instead of Hermite-Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.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
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
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
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
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
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
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
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
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
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
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
This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewp...This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.展开更多
A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart...A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.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
A novel method of anti-reverberation based on the fractional Fourier transformation is presented. By virtue of the fact that it has a good focus property in the fractional Fourier domain, the linearly frequency modula...A novel method of anti-reverberation based on the fractional Fourier transformation is presented. By virtue of the fact that it has a good focus property in the fractional Fourier domain, the linearly frequency modulation (LFM) signal can be seperated from the reverberation through a swept-frequency filter. With the actual reverberation data and the LFM pulse for seperation, the good results are obtained: the reverbareation is largely removed, and relatively the better performance is shown under the lower signal reverberation ratio (SRR). Based on the theorical analyses and simulation results, two schemes for detecting targets are provided: one is the detection of the LFM echo from the target with a threshold by means of this method directly; the other is to detect the target by means of other methods, with this method performing pre-process to increase SRR, which need enough large SRR.展开更多
Tensor analysis approaches are of great importance in various fields such as computa-tion vision and signal processing.Thereinto,the definitions of tensor-tensor product(t-product)and tensor singular value decompositi...Tensor analysis approaches are of great importance in various fields such as computa-tion vision and signal processing.Thereinto,the definitions of tensor-tensor product(t-product)and tensor singular value decomposition(t-SVD)are significant in practice.This work presents new t-product and t-SVD definitions based on the discrete simplified fractional Fourier transform(DSFRFT).The proposed definitions can effectively deal with special complex tenors,which fur-ther motivates the transform based tensor analysis approaches.Then,we define a new tensor nucle-ar norm induced by the DSFRFT based t-SVD.In addition,we analyze the computational complex-ity of the proposed t-SVD,which indicates that the proposed t-SVD can improve the computation-al efficiency.展开更多
With the increasing requirement of military and security, the technology of information hiding for speech becomes a hotspot and difficulty in the fields of speech signal processing and in-formation security, which is ...With the increasing requirement of military and security, the technology of information hiding for speech becomes a hotspot and difficulty in the fields of speech signal processing and in-formation security, which is developing rapidly. In order to stand against the stegano-analysis, the paper proposed an optimal information hiding algorithm for speech in the Fractional Fourier Transform (FrFT) domain based on the Minimum Mean Square Error (MMSE) criterion. The results of simulation and experiments show that speech modified by the proposed algorithm has no remarkable changes both in time and frequency domains, which can effectively resist the time and frequency analysis, Otherwise, the algorithm is robust to general signal process attack, and the difference is imperceptible between the original and modified speech.展开更多
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Project supported by the Young People Foundation of Zhejiang Normal University, China (Grant No KYJ06Y07150)
文摘This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L^2(R) instead of Hermite-Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
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 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.
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.
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.
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.
文摘This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.
基金Sponsored by the National Natural Science Foundation of China(60605015)
文摘A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.
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.
文摘A novel method of anti-reverberation based on the fractional Fourier transformation is presented. By virtue of the fact that it has a good focus property in the fractional Fourier domain, the linearly frequency modulation (LFM) signal can be seperated from the reverberation through a swept-frequency filter. With the actual reverberation data and the LFM pulse for seperation, the good results are obtained: the reverbareation is largely removed, and relatively the better performance is shown under the lower signal reverberation ratio (SRR). Based on the theorical analyses and simulation results, two schemes for detecting targets are provided: one is the detection of the LFM echo from the target with a threshold by means of this method directly; the other is to detect the target by means of other methods, with this method performing pre-process to increase SRR, which need enough large SRR.
基金supported by the National Key R&D Program of China(No.2018YFC2000600).
文摘Tensor analysis approaches are of great importance in various fields such as computa-tion vision and signal processing.Thereinto,the definitions of tensor-tensor product(t-product)and tensor singular value decomposition(t-SVD)are significant in practice.This work presents new t-product and t-SVD definitions based on the discrete simplified fractional Fourier transform(DSFRFT).The proposed definitions can effectively deal with special complex tenors,which fur-ther motivates the transform based tensor analysis approaches.Then,we define a new tensor nucle-ar norm induced by the DSFRFT based t-SVD.In addition,we analyze the computational complex-ity of the proposed t-SVD,which indicates that the proposed t-SVD can improve the computation-al efficiency.
基金Supported by the National Natural Science Foundation of China (No. 60472058, No. 60975017)Jiangsu Provincial Natural Science Foundation (No. BK2008291)
文摘With the increasing requirement of military and security, the technology of information hiding for speech becomes a hotspot and difficulty in the fields of speech signal processing and in-formation security, which is developing rapidly. In order to stand against the stegano-analysis, the paper proposed an optimal information hiding algorithm for speech in the Fractional Fourier Transform (FrFT) domain based on the Minimum Mean Square Error (MMSE) criterion. The results of simulation and experiments show that speech modified by the proposed algorithm has no remarkable changes both in time and frequency domains, which can effectively resist the time and frequency analysis, Otherwise, the algorithm is robust to general signal process attack, and the difference is imperceptible between the original and modified speech.