Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent t...Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.展开更多
首先分析Chirp函数在频域上的一般特性,并且分析Altrea公司提供的数控振荡器知识产权核(NCO IP core)的输入/输出特性,通过MegaCore环境确定其输入控制字,通过外围逻辑电路实时向NCO IP core调入控制频率控制字以达到改变输出频率的目的...首先分析Chirp函数在频域上的一般特性,并且分析Altrea公司提供的数控振荡器知识产权核(NCO IP core)的输入/输出特性,通过MegaCore环境确定其输入控制字,通过外围逻辑电路实时向NCO IP core调入控制频率控制字以达到改变输出频率的目的,并通过在示波器上观测FPGA的运行情况,验证了该设计具有很好的输出效果。展开更多
A simple identification method based on a closed-loop experiment is proposed to measure the infinity norm of sensitivity function.A chirp signal,modified to have desired band-limited characteristic and finite duration...A simple identification method based on a closed-loop experiment is proposed to measure the infinity norm of sensitivity function.A chirp signal,modified to have desired band-limited characteristic and finite duration,is used as the excitation in the experiment,and the sensitivity function is calculated using Fourier transform of input and error signals before the infinity norm is evaluated through maximization of the magnitude of sensitivity function.With an additional feature of providing values of gain margin and phase margin at a little extra effort,this method can be used in the identification step of a controller auto-tuning procedure,as having been supported by simulation results showing its capability of providing fast and accurate estimates for a large variety of processes.展开更多
文摘Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.
文摘首先分析Chirp函数在频域上的一般特性,并且分析Altrea公司提供的数控振荡器知识产权核(NCO IP core)的输入/输出特性,通过MegaCore环境确定其输入控制字,通过外围逻辑电路实时向NCO IP core调入控制频率控制字以达到改变输出频率的目的,并通过在示波器上观测FPGA的运行情况,验证了该设计具有很好的输出效果。
基金Sponsored by the Key Construction Program of the"985"Program (1010012047201)
文摘A simple identification method based on a closed-loop experiment is proposed to measure the infinity norm of sensitivity function.A chirp signal,modified to have desired band-limited characteristic and finite duration,is used as the excitation in the experiment,and the sensitivity function is calculated using Fourier transform of input and error signals before the infinity norm is evaluated through maximization of the magnitude of sensitivity function.With an additional feature of providing values of gain margin and phase margin at a little extra effort,this method can be used in the identification step of a controller auto-tuning procedure,as having been supported by simulation results showing its capability of providing fast and accurate estimates for a large variety of processes.
