数学物理方程-第8讲(3[1].3-3.3)-texed

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2、{Þ~½ÂµFáC(FourierTransform)f(x)3(−∞,+∞)þýéȧPZ+∞g(ω)=f(x)e−jωxdx−∞KkZ+∞f(x)=1g(ω)ejωxdω2π−∞·¡g(ω)f(x)Fá(Fourier)C§PF[f]"¡f(x)g(ω)Fá_C§PF−1[f]"¡´(®ÏÆnÆ)êÆÔn§AϼêNovember12,20084/38JeanBaptisteJosephFourier¨FáBorn:21March1768,inAuxerre,Bourgogne,France¡´(®ÏÆnÆ)êÆÔn§AϼêNovember12,2

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7、xf(x)]=dF[f(x)]dωòÈ5µf1(x)∗f2(x)=f2(x)∗f1(x)[f1(x)∗f2(x)]∗f3(x)=f2(x)∗[f1(x)∗f3(x)]¡´(®ÏÆnÆ)êÆÔn§AϼêNovember12,20087/38§3.3È©C{Þ~FáC5µF[αf1+βf2]=αF[f1]+βF[f2]£55¤F[f0(x)]=jωF[f(x)]£©5¤íííØØصµµF[f(n)(x)]=(jω)nF[f(x)]F[−jxf(x)]=dF[f(x)]dωòÈ5µf1(x)∗f2(x)=f2(x)∗