广义Fourier正弦、余弦变换研究  

Research on sine and cosine transform of broad sense Fourier

作　　者：李海涛[1] 付立志[1] 

机构地区：[1]焦作大学基础系,河南焦作454003

出　　处：《河南理工大学学报（自然科学版）》2009年第4期540-542,共3页Journal of Henan Polytechnic University（Natural Science）

基　　金：河南省教育厅自然科学研究计划项目(2008C110003);河南省高等教育教学成果鉴定项目(豫高教改鉴字〔2008〕845号);河南省科学技术成果项目(9412008J0758)

摘　　要：通过定义广义余弦和正弦变换,利用函数的奇偶性,探讨了广义余弦、正弦变换与全时域下广义Fourier变换的对应关系以及广义余弦、正弦变换的对称性.在对单位阶跃函数在广义Fourier变换中的屏蔽效应进行研究基础上,探讨了半屏定理结果中冲激函数项、一般函数项与广义余弦、正弦变换的交叉对应关系,得到了它们之间相互制约的规律性结论.By defining the generalized cosine, sine transform and using the pairity of function, the corresponding relations between the generalized cosine, sine transform and the generalized Fourier transform under full time domain are discussed, as well as the symmetry of the generalized cosine and sine transform. Meanwhile on the basis of research on the shielded effect of unit step function in generalized Fourier transform, the crossing and corresponding relations between the impulse function and common function under the half - shielded principle, the generalized cosine and sine transform are explored. The regularity conclusions of inter - restriction relations between them are bbtained.

关 键 词：广义FOURIER变换 余弦变换 正弦变换 对应关系 制约性 HILBERT变换 

分 类 号：O174.22[理学—数学]