Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image w...Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.展开更多
Present study emphasizes the applicability of linear theory concept onto hilly watersheds. For this purpose, Z-transform technique was used to derive the instantaneous unit hydrograph (IUH) from the transfer function ...Present study emphasizes the applicability of linear theory concept onto hilly watersheds. For this purpose, Z-transform technique was used to derive the instantaneous unit hydrograph (IUH) from the transfer function of autoregressive and moving average (ARMA) type linear difference equation. Parameters of the ARMA type rainfall-runoff process were estimated by least-squares method. The derived IUH from Z-transform (i.e. ARMA-IUH) has been used to compute the hydrologic response i.e. direct runoff hydrograph (DRH). Fur-ther, the superiority of the proposed approach has been tested by comparing the results through the results obtained from the Nash-IUH. Analyzing the results obtained from ARMA-IUH and Nash-IUH for the two hilly watersheds of North Western Himalayas shows the applicability of the linear theory concept even in turbulent flow conditions which are frequently encountered in hilly terrains under similar conditions of flow.展开更多
The electromagnetic propagation through an inhomogeneous magnetized plasma slab is studied using the Z-transform formulation of the Finite-Difference Time-Domain(FDTD) method. The direction of electromagnetic propagat...The electromagnetic propagation through an inhomogeneous magnetized plasma slab is studied using the Z-transform formulation of the Finite-Difference Time-Domain(FDTD) method. The direction of electromagnetic propagation is parallel to the biasing magnetic filed. To validate the Z-transform algorithm, the reflection and transmission coefficients for the right-hand circularly polarized wave of the homogeneous magnetized plasma slab are computed by means of discrete Fourier transform. The comparison between the reflection and transmission coefficients of the homogeneous plasma slab and analytical values indicates that Z-transform algorithm is very accurate. When the plasma frequency varies according to the square root and parabolic relations, the reflection and transmission coefficients of the inhomogeneous magnetized plasma slab are computed.展开更多
This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transform...This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.展开更多
To discuss the relationship between stability and bullwhip effect in the supply chain system,a basic model in a production-inventory control system is developed using difference equations.Z-transform techniques are ap...To discuss the relationship between stability and bullwhip effect in the supply chain system,a basic model in a production-inventory control system is developed using difference equations.Z-transform techniques are applied to investigate the production ordering and inventory dynamics.For the two operational regimes of sufficient inventory coverage and insufficient inventory coverage,the scope of decision parameters which make the system stable or instable is investigated.Under two operational regimes and the actual system,production release rates,stability/instability and bullwhip effect in the stable region and instable region are examined based on different demand functions,and then the numerical simulation results are given.The results show that reasonable choices of fractional adjustment of inventory and supply line can make the system stable and decrease bullwhip effect.It is summarized that the piecewise linearization based on the stability analysis approach is a valid approximation to the analysis of production-inventory ordering systems with nonlinearities.Some interesting results are obtained and they have important implications for improving inventory and order decisions in supply chain systems.展开更多
A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult ...A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.展开更多
Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) t...Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging(FTDA) technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform(CZT) is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.展开更多
The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions....The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.展开更多
One of the most commonly used statistical methods is bivariate correlation analysis. However, it is usually the case that little or no attention is given to power and sample size considerations when planning a study i...One of the most commonly used statistical methods is bivariate correlation analysis. However, it is usually the case that little or no attention is given to power and sample size considerations when planning a study in which correlation will be the primary analysis. In fact, when we reviewed studies published in clinical research journals in 2014, we found that none of the 111 articles that presented results of correlation analyses included a sample size justification. It is sometimes of interest to compare two correlation coefficients between independent groups. For example, one may wish to compare diabetics and non-diabetics in terms of the correlation of systolic blood pressure with age. Tools for performing power and sample size calculations for the comparison of two independent Pearson correlation coefficients are widely available;however, we were unable to identify any easily accessible tools for power and sample size calculations when comparing two independent Spearman rank correlation coefficients or two independent Kendall coefficients of concordance. In this article, we provide formulas and charts that can be used to calculate the sample size that is needed when testing the hypothesis that two independent Spearman or Kendall coefficients are equal.展开更多
The roll angular rate is much crucial for the guidance and control of the projectile.Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate.Neverthele...The roll angular rate is much crucial for the guidance and control of the projectile.Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate.Nevertheless,the radial magnetometer signal is modulated by the high-speed rotation,thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal.The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate.To reach this goal,a modified spline-kernelled chirplet transform(MSCT)algorithm is proposed in this paper.Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal,the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane,thereby leading to a terrible instantaneous frequency extraction accuracy.However,the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform.The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel.Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution,the MSCT can obtain a more precise instantaneous frequency.The performance of the MSCT was evaluated by a series of numerical simulations,high-speed turntable experiments,and real flight tests.The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal,and can accurately extract the roll angular rate for the high spinning projectiles.展开更多
A method of describing one-dimensional photonic crystals (1DPCs) based on Z-domain digital signal processing theory is presented. The analytical expression of the target band gap spectrum in the digital domain is ob...A method of describing one-dimensional photonic crystals (1DPCs) based on Z-domain digital signal processing theory is presented. The analytical expression of the target band gap spectrum in the digital domain is obtained by the autocorrelation of its impulse response. The feasibility of this method is verified by reconstructing two simple 1DPC structures with a target photonic band gap obtained by the traditional transfer matrix method. This method provides an effective approach to function-guided designs of interference-based band gap structures for photonic applications.展开更多
Programmable photonic waveguide meshes can be programmed into many different circuit topologies and thereby provide a variety of functions.Due to the complexity of the signal routing in a general mesh,a particular syn...Programmable photonic waveguide meshes can be programmed into many different circuit topologies and thereby provide a variety of functions.Due to the complexity of the signal routing in a general mesh,a particular synthesis algorithm often only accounts for a specific function with a specific cell configuration.In this paper,we try to synthesize the programmable waveguide mesh to support multiple configurations with a more general digital signal processing platform.To show the feasibility of this technique,photonic waveguide meshes in different configurations(square,triangular and hexagonal meshes)are designed to realize optical signal interleaving with arbitrary duty cycles.The digital signal processing(DSP)approach offers an effective pathway for the establishment of a general design platform for the software-defined programmable photonic integrated circuits.The use of well-developed DSP techniques and algorithms establishes a link between optical and electrical signals and makes it convenient to realize the computer-aided design of optics–electronics hybrid systems.展开更多
We introduce a general framework for the log-time sampling of continuous-time signals. We define the zeta transform based on the log-time sampling scheme, where the signal x(t)is sampled at time instants tn=Tlogn,n=1,...We introduce a general framework for the log-time sampling of continuous-time signals. We define the zeta transform based on the log-time sampling scheme, where the signal x(t)is sampled at time instants tn=Tlogn,n=1,2,....The zeta transform of the log-time sampled signals can be described by a linear combination of Riemann zeta function, which firmly joins the log-time sampling process to the number theory. The instantaneous sampling frequency of the log-sampled signal equals fn=n/T,n=1,2,..., i.e. it increases linearly with the sampling number. We describe the properties of the log-sampled signals and discuss several applications in nonuniform sampling schemes.展开更多
The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using po...The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using power converters they can be strongly non-harmonic, sometimes piecewise constants with zero spaces between them. Then, one deals with power series of time pulses. The impulse switching functions which are orthogonal ones can be derived from these series. The new impulse switching functions are created using Z-transform, inverse Z-transform and numerical series/sequences. The impulse switching functions created this way can be used for both steady- and transient state investigation of converters.展开更多
We present a numerical study of the resolution power of Padé Approximations to the Z-transform, compared to the Fourier transform. As signals are represented as isolated poles of the Padé Approximant to the ...We present a numerical study of the resolution power of Padé Approximations to the Z-transform, compared to the Fourier transform. As signals are represented as isolated poles of the Padé Approximant to the Z-transform, resolution depends on the relative position of signal poles in the complex plane i.e. not only the difference in frequency (separation in angular position) but also the difference in the decay constant (separation in radial position) contributes to the resolution. The frequency resolution increase reported by other authors is therefore an upper limit: in the case of signals with different decay rates frequency resolution can be further increased.展开更多
The convolution of two rational transfer functions is also rational, but a formula for the convolution has never been derived. This paper introduces a formula for the convolution of two rational functions in the frequ...The convolution of two rational transfer functions is also rational, but a formula for the convolution has never been derived. This paper introduces a formula for the convolution of two rational functions in the frequency domain by two new methods. The first method involves a partial fraction expansion of the rational transfer functions where the problem gets reduced to the sum of the convolution of the partial fractions of the two functions, each of which can be solved by a new formula. Since the calculation of the roots of a high-order polynomial can be very time-consuming, we also demonstrate new methods for performing the convolution without calculating these roots or undergoing partial fraction expansion. The convolution of two rational Laplace transform denominators can be calculated using their resultant, while that of the two rational Z-transform transfer functions can be found using Newton’s identities. The numerator can be easily found by multiplying the numerator with the initial values of the power series of the result.展开更多
Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the s...Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the smallest size is called the forcing number of M,denoted by f(G,M).The forcing spectrum of G is defined as:Spec(G)={f(G,M)|M is a perfect matching of G}.In this paper,by applying the Ztransformation graph(resonance graph)we show that for any polyomino with perfect matchings and any even polygonal chain,their forcing spectra are integral intervals.Further we obtain some sharp bounds on maximum and minimum forcing numbers of hexagonal chains with given number of kinks.Forcing spectra of two extremal chains are determined.展开更多
This paper considers a discrete-time Geo/G/1 queue under the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of ...This paper considers a discrete-time Geo/G/1 queue under the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N, D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n+. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n+ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.展开更多
In [1], we introduced the concept of z-transformation graphs of perfect matchings of hexagonal systems and showed that the z-transformation graph of perfect matchings of a hexagonal system has at most two vertices of...In [1], we introduced the concept of z-transformation graphs of perfect matchings of hexagonal systems and showed that the z-transformation graph of perfect matchings of a hexagonal system has at most two vertices of degree one. In this paper, we enumerate the hexagonal systems whose z-transformation graphs have a vertex of degree one. In particular, such hexagonal systems with various symmetries are also enumerated.展开更多
文摘Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.
文摘Present study emphasizes the applicability of linear theory concept onto hilly watersheds. For this purpose, Z-transform technique was used to derive the instantaneous unit hydrograph (IUH) from the transfer function of autoregressive and moving average (ARMA) type linear difference equation. Parameters of the ARMA type rainfall-runoff process were estimated by least-squares method. The derived IUH from Z-transform (i.e. ARMA-IUH) has been used to compute the hydrologic response i.e. direct runoff hydrograph (DRH). Fur-ther, the superiority of the proposed approach has been tested by comparing the results through the results obtained from the Nash-IUH. Analyzing the results obtained from ARMA-IUH and Nash-IUH for the two hilly watersheds of North Western Himalayas shows the applicability of the linear theory concept even in turbulent flow conditions which are frequently encountered in hilly terrains under similar conditions of flow.
基金Supported by the National Natural Science Foundation of China (No.10375071 and No.60271027)Foundation of Key Lab of Electromagnetic Environment (No.51486020203 ZK1301)
文摘The electromagnetic propagation through an inhomogeneous magnetized plasma slab is studied using the Z-transform formulation of the Finite-Difference Time-Domain(FDTD) method. The direction of electromagnetic propagation is parallel to the biasing magnetic filed. To validate the Z-transform algorithm, the reflection and transmission coefficients for the right-hand circularly polarized wave of the homogeneous magnetized plasma slab are computed by means of discrete Fourier transform. The comparison between the reflection and transmission coefficients of the homogeneous plasma slab and analytical values indicates that Z-transform algorithm is very accurate. When the plasma frequency varies according to the square root and parabolic relations, the reflection and transmission coefficients of the inhomogeneous magnetized plasma slab are computed.
文摘This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.
文摘To discuss the relationship between stability and bullwhip effect in the supply chain system,a basic model in a production-inventory control system is developed using difference equations.Z-transform techniques are applied to investigate the production ordering and inventory dynamics.For the two operational regimes of sufficient inventory coverage and insufficient inventory coverage,the scope of decision parameters which make the system stable or instable is investigated.Under two operational regimes and the actual system,production release rates,stability/instability and bullwhip effect in the stable region and instable region are examined based on different demand functions,and then the numerical simulation results are given.The results show that reasonable choices of fractional adjustment of inventory and supply line can make the system stable and decrease bullwhip effect.It is summarized that the piecewise linearization based on the stability analysis approach is a valid approximation to the analysis of production-inventory ordering systems with nonlinearities.Some interesting results are obtained and they have important implications for improving inventory and order decisions in supply chain systems.
文摘A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.
基金supported by National Natural Science Foundation of China(Grant Nos.5112502251005173)+1 种基金PhD Programs Foundation of Ministry of Education of China(Grant No.20110201110025)the Fundamental Research Funds for the Central Universities of China
文摘Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging(FTDA) technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform(CZT) is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.
基金Jiwei Zhang is partially supported by the National Natural Science Foundation of China under Grant No.11771035the NSAF U1530401+3 种基金the Natural Science Foundation of Hubei Province No.2019CFA007Xiangtan University 2018ICIP01Chunxiong Zheng is partially supported by Natural Science Foundation of Xinjiang Autonom ous Region under No.2019D01C026the National Natural Science Foundation of China under Grant Nos.11771248 and 91630205。
文摘The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.
文摘One of the most commonly used statistical methods is bivariate correlation analysis. However, it is usually the case that little or no attention is given to power and sample size considerations when planning a study in which correlation will be the primary analysis. In fact, when we reviewed studies published in clinical research journals in 2014, we found that none of the 111 articles that presented results of correlation analyses included a sample size justification. It is sometimes of interest to compare two correlation coefficients between independent groups. For example, one may wish to compare diabetics and non-diabetics in terms of the correlation of systolic blood pressure with age. Tools for performing power and sample size calculations for the comparison of two independent Pearson correlation coefficients are widely available;however, we were unable to identify any easily accessible tools for power and sample size calculations when comparing two independent Spearman rank correlation coefficients or two independent Kendall coefficients of concordance. In this article, we provide formulas and charts that can be used to calculate the sample size that is needed when testing the hypothesis that two independent Spearman or Kendall coefficients are equal.
基金National Natural Science Foundation(NNSF)of China under Grant 61771059National Natural Science Foundation(NNSF)of China under Grant 61471046Beijing Natural Science Foundation under Grant 4172022 to provide fund for conducting experiments。
文摘The roll angular rate is much crucial for the guidance and control of the projectile.Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate.Nevertheless,the radial magnetometer signal is modulated by the high-speed rotation,thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal.The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate.To reach this goal,a modified spline-kernelled chirplet transform(MSCT)algorithm is proposed in this paper.Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal,the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane,thereby leading to a terrible instantaneous frequency extraction accuracy.However,the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform.The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel.Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution,the MSCT can obtain a more precise instantaneous frequency.The performance of the MSCT was evaluated by a series of numerical simulations,high-speed turntable experiments,and real flight tests.The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal,and can accurately extract the roll angular rate for the high spinning projectiles.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10804070 and 61137002)the Key Program of the Science and Technology Commission of Shanghai,China(Grant No.11jc1413300)the Shanghai Leading Academic Discipline Project,China(Grant No.S30108)
文摘A method of describing one-dimensional photonic crystals (1DPCs) based on Z-domain digital signal processing theory is presented. The analytical expression of the target band gap spectrum in the digital domain is obtained by the autocorrelation of its impulse response. The feasibility of this method is verified by reconstructing two simple 1DPC structures with a target photonic band gap obtained by the traditional transfer matrix method. This method provides an effective approach to function-guided designs of interference-based band gap structures for photonic applications.
文摘Programmable photonic waveguide meshes can be programmed into many different circuit topologies and thereby provide a variety of functions.Due to the complexity of the signal routing in a general mesh,a particular synthesis algorithm often only accounts for a specific function with a specific cell configuration.In this paper,we try to synthesize the programmable waveguide mesh to support multiple configurations with a more general digital signal processing platform.To show the feasibility of this technique,photonic waveguide meshes in different configurations(square,triangular and hexagonal meshes)are designed to realize optical signal interleaving with arbitrary duty cycles.The digital signal processing(DSP)approach offers an effective pathway for the establishment of a general design platform for the software-defined programmable photonic integrated circuits.The use of well-developed DSP techniques and algorithms establishes a link between optical and electrical signals and makes it convenient to realize the computer-aided design of optics–electronics hybrid systems.
文摘We introduce a general framework for the log-time sampling of continuous-time signals. We define the zeta transform based on the log-time sampling scheme, where the signal x(t)is sampled at time instants tn=Tlogn,n=1,2,....The zeta transform of the log-time sampled signals can be described by a linear combination of Riemann zeta function, which firmly joins the log-time sampling process to the number theory. The instantaneous sampling frequency of the log-sampled signal equals fn=n/T,n=1,2,..., i.e. it increases linearly with the sampling number. We describe the properties of the log-sampled signals and discuss several applications in nonuniform sampling schemes.
文摘The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using power converters they can be strongly non-harmonic, sometimes piecewise constants with zero spaces between them. Then, one deals with power series of time pulses. The impulse switching functions which are orthogonal ones can be derived from these series. The new impulse switching functions are created using Z-transform, inverse Z-transform and numerical series/sequences. The impulse switching functions created this way can be used for both steady- and transient state investigation of converters.
文摘We present a numerical study of the resolution power of Padé Approximations to the Z-transform, compared to the Fourier transform. As signals are represented as isolated poles of the Padé Approximant to the Z-transform, resolution depends on the relative position of signal poles in the complex plane i.e. not only the difference in frequency (separation in angular position) but also the difference in the decay constant (separation in radial position) contributes to the resolution. The frequency resolution increase reported by other authors is therefore an upper limit: in the case of signals with different decay rates frequency resolution can be further increased.
文摘The convolution of two rational transfer functions is also rational, but a formula for the convolution has never been derived. This paper introduces a formula for the convolution of two rational functions in the frequency domain by two new methods. The first method involves a partial fraction expansion of the rational transfer functions where the problem gets reduced to the sum of the convolution of the partial fractions of the two functions, each of which can be solved by a new formula. Since the calculation of the roots of a high-order polynomial can be very time-consuming, we also demonstrate new methods for performing the convolution without calculating these roots or undergoing partial fraction expansion. The convolution of two rational Laplace transform denominators can be calculated using their resultant, while that of the two rational Z-transform transfer functions can be found using Newton’s identities. The numerator can be easily found by multiplying the numerator with the initial values of the power series of the result.
基金supported by the National Natural Science Foundation of China(Nos.11871256,11371180,11226286)。
文摘Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the smallest size is called the forcing number of M,denoted by f(G,M).The forcing spectrum of G is defined as:Spec(G)={f(G,M)|M is a perfect matching of G}.In this paper,by applying the Ztransformation graph(resonance graph)we show that for any polyomino with perfect matchings and any even polygonal chain,their forcing spectra are integral intervals.Further we obtain some sharp bounds on maximum and minimum forcing numbers of hexagonal chains with given number of kinks.Forcing spectra of two extremal chains are determined.
基金supported by the National Natural Science Foundation of China under Grant Nos.71171138,71301111,71571127the Scientific Research Innovation&Application Foundation of Headmaster of Hexi University under Grant Nos.XZ2013-06,XZ2013-09
文摘This paper considers a discrete-time Geo/G/1 queue under the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N, D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n+. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n+ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.
基金This work is supported by the National Natural Sciences Foundation China.
文摘In [1], we introduced the concept of z-transformation graphs of perfect matchings of hexagonal systems and showed that the z-transformation graph of perfect matchings of a hexagonal system has at most two vertices of degree one. In this paper, we enumerate the hexagonal systems whose z-transformation graphs have a vertex of degree one. In particular, such hexagonal systems with various symmetries are also enumerated.