This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic d...This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.展开更多
Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properti...Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.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
This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate ...This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution.Indeed,Schauder and Banach fixed point theorems are utilized to prove our claim.Further,an algorithm for the approximate analytical solution to the proposed problem has been established.In this regard,the conformable fractional differential transform(CFDT)technique is used to compute the required results in the form of a series.Using Matlab-16,we simulate the series solution to illustrate our results graphically.Finally,a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.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
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
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
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 pow...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
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...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 be 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
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie...This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.展开更多
Nowadays,one of the most important difficulties is the protection and privacy of confidential data.To address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illeg...Nowadays,one of the most important difficulties is the protection and privacy of confidential data.To address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illegal activities and assaults.Modern cryptographic ciphers use the non-linear component of block cipher to ensure the robust encryption process and lawful decoding of plain data during the decryption phase.For the designing of a secure substitution box(S-box),non-linearity(NL)which is an algebraic property of the S-box has great importance.Consequently,the main focus of cryptographers is to achieve the S-box with a high value of non-linearity.In this suggested study,an algebraic approach for the construction of 16×16 S-boxes is provided which is based on the fractional transformation Q(z)=1/α(z)^(m)+β(mod257)and finite field.This technique is only applicable for the even number exponent in the range(2-254)that are not multiples of 4.Firstly,we choose a quadratic fractional transformation,swap each missing element with repeating elements,and acquire the initial S-box.In the second stage,a special permutation of the symmetric group S256 is utilized to construct the final S-box,which has a higher NL score of 112.75 than the Advanced Encryption Standard(AES)S-box and a lower linear probability score of 0.1328.In addition,a tabular and graphical comparison of various algebraic features of the created S-box with many other S-boxes from the literature is provided which verifies that the created S-box has the ability and is good enough to withstand linear and differential attacks.From different analyses,it is ensured that the proposed S-boxes are better than as compared to the existing S-boxes.Further these S-boxes can be utilized in the security of the image data and the text data.展开更多
This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,w...This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.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
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 coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Kl...In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.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
This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The propos...This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.展开更多
Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR)data pre-processing.The most commonly used least squares(LS)method,although satisfying the real-time requirement,has many problems such ...Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR)data pre-processing.The most commonly used least squares(LS)method,although satisfying the real-time requirement,has many problems such as highly correlated initial values of the expression parameters,the need to pre-estimate the trend term shape,and poor fitting accuracy at low signal-to-noise ratios.In order to achieve real-time and robust trend term removal,a new trend term removal method using genetic programming(GP)in symbolic regression is constructed in this paper,and the FTIR simulation interference results and experimental measurement data for common volatile organic compounds(VOCs)gases are analyzed.The results show that the genetic programming algorithm can both reduce the initial value requirement and greatly improve the trend term accuracy by 20%-30% in three evaluation indicators,which is suitable for gas FTIR detection in complex scenarios.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
文摘This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.
文摘Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.
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.
文摘This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution.Indeed,Schauder and Banach fixed point theorems are utilized to prove our claim.Further,an algorithm for the approximate analytical solution to the proposed problem has been established.In this regard,the conformable fractional differential transform(CFDT)technique is used to compute the required results in the form of a series.Using Matlab-16,we simulate the series solution to illustrate our results graphically.Finally,a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.
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 (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 be 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 Deanship of Scientific Research at King Khalid University,Saudi Arabia (R.G.P.1/207/43)。
文摘This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.
基金The authors received the funding for this study from King Saud University,Riyadh,Saudi Arabia under the research supporting project Number RSP 2023R167.Sameh Askar received this grant from King Saud University。
文摘Nowadays,one of the most important difficulties is the protection and privacy of confidential data.To address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illegal activities and assaults.Modern cryptographic ciphers use the non-linear component of block cipher to ensure the robust encryption process and lawful decoding of plain data during the decryption phase.For the designing of a secure substitution box(S-box),non-linearity(NL)which is an algebraic property of the S-box has great importance.Consequently,the main focus of cryptographers is to achieve the S-box with a high value of non-linearity.In this suggested study,an algebraic approach for the construction of 16×16 S-boxes is provided which is based on the fractional transformation Q(z)=1/α(z)^(m)+β(mod257)and finite field.This technique is only applicable for the even number exponent in the range(2-254)that are not multiples of 4.Firstly,we choose a quadratic fractional transformation,swap each missing element with repeating elements,and acquire the initial S-box.In the second stage,a special permutation of the symmetric group S256 is utilized to construct the final S-box,which has a higher NL score of 112.75 than the Advanced Encryption Standard(AES)S-box and a lower linear probability score of 0.1328.In addition,a tabular and graphical comparison of various algebraic features of the created S-box with many other S-boxes from the literature is provided which verifies that the created S-box has the ability and is good enough to withstand linear and differential attacks.From different analyses,it is ensured that the proposed S-boxes are better than as compared to the existing S-boxes.Further these S-boxes can be utilized in the security of the image data and the text data.
基金funded by the Deanship of Research in Zarqa University,Jordan。
文摘This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.
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 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 coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.
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This research was funded by Deanship of Scientific Research,Taif University Researches Supporting Project number(TURSP-2020/216),Taif University,Taif,Saudi Arabia.
文摘This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.
基金supported by JKW Program(No.M102-03)National Program(No.E0F80246).
文摘Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR)data pre-processing.The most commonly used least squares(LS)method,although satisfying the real-time requirement,has many problems such as highly correlated initial values of the expression parameters,the need to pre-estimate the trend term shape,and poor fitting accuracy at low signal-to-noise ratios.In order to achieve real-time and robust trend term removal,a new trend term removal method using genetic programming(GP)in symbolic regression is constructed in this paper,and the FTIR simulation interference results and experimental measurement data for common volatile organic compounds(VOCs)gases are analyzed.The results show that the genetic programming algorithm can both reduce the initial value requirement and greatly improve the trend term accuracy by 20%-30% in three evaluation indicators,which is suitable for gas FTIR detection in complex scenarios.
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.