摘要
基于三角插值理论,用函数的三角插值函数代替函数本身,并借助Dirac广义函数的性质写出三角插值函数的Fourier变换、逆变换的解析表达式,将之作为函数的Fourier变换、逆变换的近似。基于这种想法,分别推导一元函数、二元函数的Fourier变换和Fourier逆变换的计算公式。数值实验表明,这种方法比通常基于矩形求积公式计算连续Fourier变换、逆变换的精度要高。
Based on the trigonometric interpolation theory,a function is approximated by its trigonometric interpolation function.By the properties of Dirac distribution function,the analytic expressions of the Fourier transform and inverse Fourier transform for the trigonometric interpolation function are derived to approximate the Fourier transform and inverse Fourier transform for the original function.The numerical formulations for calculating the Fourier trans-forms and the inverse Fourier transforms of the functions with one variable and two variables are derived,respec-tively.Comparing with the algorithm using rectangular formula of numerical integration,the numerical examples show that the proposed method achieves higher accuracy.
作者
魏鑫宇
冯立新
张国艳
WEI Xin-yu;FENG Li-xin;ZHANG Guo-yan(School of Mathematical Science,Heilongjiang University,Harbin 150080,China;Department of Mechanical and Electronic Engineering,HarbinHuaxia Computer Vocational and Technical College,Harbin 150025,China)
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2012年第3期303-307,312,共6页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(10801046)
黑龙江大学创新团队资助项目(Hdtd2010-14)
黑龙江省教育厅科学技术项目(12521429)
