令 [tex=11.0x3.643]bjml32B4+bSxhXIAnkK4fGwsWBspDO6dXHP+JXtph84LWjQSLJpg8p9oNLhhAECy/3iJ/882TcP6z/R6CjJlKtc3oKFjKoK9/7lPtOTUlMQGFwqU8WuKTGgeC0/2QcfJ[/tex]是一个基波周期 [tex=2.5x1.286]eVmCSibeu8KmlUXKCNKfdg==[/tex] 的周期信号,傅里叶系数为 [tex=1.0x1.286]bjRZm1Vy1zu4e3/HqyedUQ==[/tex] 。(a) 求 [tex=0.929x1.286]i1uEzrKUlskuljI2i7/RsQ==[/tex] ;( b ) 求 [tex=3.571x1.286]Ava2Z+x8eqeSZDsdmxSndqEm9MTValO/tubQK7Ac7N0=[/tex]的傅里叶级数表示 ;( c ) 利用 ( b ) 的结果和连续时间傅里叶级数的微分性质求 [tex=1.643x1.286]yTgjuw3VOLhYFI7hLX2LPg==[/tex] 的傅里叶级数系数。

2022-06-09

令 [tex=11.0x3.643]bjml32B4+bSxhXIAnkK4fGwsWBspDO6dXHP+JXtph84LWjQSLJpg8p9oNLhhAECy/3iJ/882TcP6z/R6CjJlKtc3oKFjKoK9/7lPtOTUlMQGFwqU8WuKTGgeC0/2QcfJ[/tex]是一个基波周期 [tex=2.5x1.286]eVmCSibeu8KmlUXKCNKfdg==[/tex] 的周期信号,傅里叶系数为 [tex=1.0x1.286]bjRZm1Vy1zu4e3/HqyedUQ==[/tex] 。(a) 求 [tex=0.929x1.286]i1uEzrKUlskuljI2i7/RsQ==[/tex] ;( b ) 求 [tex=3.571x1.286]Ava2Z+x8eqeSZDsdmxSndqEm9MTValO/tubQK7Ac7N0=[/tex]的傅里叶级数表示 ;( c ) 利用 ( b ) 的结果和连续时间傅里叶级数的微分性质求 [tex=1.643x1.286]yTgjuw3VOLhYFI7hLX2LPg==[/tex] 的傅里叶级数系数。

答案：

解(a)  [tex=7.214x2.214]e96PIA7pzdGRYtHpqJgoPPcsARwZI7dqGG/oIguTy6flfpgecjGDdtZbpzJp/J0v[/tex][tex=21.0x2.429]QhSn3nQm91RWQg5gFzFNUOcMHnP5rEoeecKh5sPmWRVBi5IhHqbKPeDFyq7mpuqseKMotdghMW3Ax0bBJkxSCmrMcu/O1hpLUVI5m28rfk8ZNk1hr0OBeT2PcfpkAtrNq+fM1PAjlzdhcsP2bSs09w==[/tex](b)  [tex=13.857x3.643]NoiXhil/ZyHX/P+ynz+8jF3DmtzpWo8Lheh7ldSffslYttUsvGlFN2S2lTaLXK7IMBqjbOfuu2BJWgyAk/qMTihl54rcX/Hcd0voha1FQO+YhOK0lIdY9LSbBqOIonbnQDg00AWC7K4ZXtZKCcs9pw==[/tex]设  [tex=4.286x1.357]3uLpjzq7X0IneRnyX/yzQGY6ab6tlkuCasbryZylXuog8zXDxunElhDVyFVuto83bJpLWIen88ITSZA3rdRnvg==[/tex], 则  [tex=11.714x2.429]i3dhwNU1Gu2Fv8HAQjFA2tL4bBUtxfPgngzvQCTKLmfr9uGesQK1nzQZoinlNOHxp0oE/qv/mzxJpBwZ8LJvDMoN6lIdrO0Oitcub99eneE=[/tex][tex=18.857x2.429]rNm3BwZwxyf6MF3ynygPEv6Hh1jWSgH4iaLAHiH/GwA4KbN9ZwGTEVEM9NlHIzOBPnBIp5WzEa2Tr1bp5EH/3DZhJcGJPwyj+5nI1yGLUmAXRPY3+587ZCRSwoS0YxBOalJ4Xhr0fYlkYzkbuqjmYK/EW6mKrm6QZFNSbSC/I90=[/tex][tex=19.071x2.357]u3Agk4Eyv4oI+gqASfCwOPGxsffsbYCsJyYTuB3WmD5/1yLZ2nY28dkmkcA8Eg7uUGo6+lvFarv5cI2uqw9NFg1qywu0Uf80WR4b3yAtKr4NVsY+I9mpao1JPpER02xNjFklYTDcLhsi2N3AERzmsjDO05KU2DRDyFsJBsXkqPM=[/tex]则 [tex=2.357x2.071]Kht1Z0eJ9XPtIQZn9QIdJ2zRoT2I6RdeFOtXzfx2l2g=[/tex] 的傅里叶级数表示式为 [tex=17.214x3.214]Kht1Z0eJ9XPtIQZn9QIdJwHB/r8KgxtQopdcbiyLBLxahm8B5qc7hRboyPh5jo5A45R/NKOsareolEqPbArT598oNpQuhK4c8KqJAXHQrYi3DMO3IZBcQld0iFkykCVlsTI+qBGB/2poev6tyZvDVGCGqRfdfHAidX5L0DTxINack52TDfnDBkNxZaFvEkZk/moxdhfMwdN6oQTIWlYiAw==[/tex](c) 因为  [tex=16.143x2.071]NoiXhil/ZyHX/P+ynz+8jJkIksUUl9HgR+O6TpQTsKi8gyjzQWWW1O3+N2Xkv1APp28qe+B/AxXqwT/vFE+wU12JPw+d+C0hoSrBiCddgpCIXITUMlG0GBfz3wMuzEg16ErUSrbjNrjdlYOFfJXl9Q==[/tex], 所以[tex=9.643x2.357]2pLeeDDfoTs/GbwezPikgN1UXRQ5Y86cJYusnz24ZQQgQvzN3x5vZyiiSLTgD2TFj3/aGl4j3tsrAM7WatYRbrj1Gy1u842jFZadevvr3rw=[/tex]

举一反三

内容

0
求下列周期函数的傅里叶级数展开式:[tex=5.571x1.286]poXx9kzw7gxFgsEa9Qp7sEY4aEblMoGWnnSty8zDy2w=[/tex]( 周期 [tex=0.643x1.286]USGVpa36zb6HMu8k0moHJA==[/tex])
1
求下列周期函数的傅里叶级数展开式：[tex=7.143x1.357]qAU07a/UMA9qmDdYIFZHiuDbQciYplFbD010frnC35s=[/tex]（周期[tex=1.071x1.0]cWYnFY7tUlCT6WhMhv7goA==[/tex]）
2
周期函数[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]的周期为[tex=1.071x1.0]cWYnFY7tUlCT6WhMhv7goA==[/tex]，试将f(x)展开成傅里叶级数，如果f(x)在[tex=2.929x1.357]FPqH6WHujNUJq9Xq0SIplg==[/tex]上的表达式为：[tex=3.929x1.5]wwWic7scd5c6929ljvvkuQ==[/tex][tex=7.0x1.357]Oy5aLxKJPd5t68LIQjG2E0wMwRmACKgIr/D8IhaESKI=[/tex] .
3
求函数系的傅里叶级数展开式:[tex=7.786x1.286]lKoao7AHJRlCMQaCikocwd9FkYgBIUtHum5SptVMYS0=[/tex],[tex=5.071x1.286]Y9nIBZA1Le7w9q8FIC0XtoPFAMFg+TzqgyUq4oFDpNDYqB7143ZGAm8mHpbxFBSP[/tex].
4
设[tex=1.714x1.357]RiG8EZN5ZhRw4jDO6I5Cvg==[/tex]为一周期信号，周期为[tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex]，其傅里叶级数的系数为[tex=1.0x1.0]0GU//5PJyC1ZogOpKG0U3A==[/tex]，试用[tex=1.0x1.0]0GU//5PJyC1ZogOpKG0U3A==[/tex]表示下列信号的傅里叶系数。[tex=3.5x1.357]BIloFusPrBF+XgL1twUxa4eqrimDwivo/Cuo3xL6JjM=[/tex]