将锯齿波展为傅里叶级数.在(0,T)这个周期上,该锯齿波可表示为[tex=4.214x1.357]2TaYAkKKz9VjYq/fHY/i0A==[/tex]
解：[tex=5.857x1.357]xhiGbZZ2zdzSYltGYi3yfQ==[/tex]，且[tex=6.5x1.357]TZmfPd/6bt/Pz9eOWB6Ym6HKgwiwpOlbrdkFGf/J9XM=[/tex]为奇函数有：[tex=10.5x3.5]EwLcuUNMJmqWR+m81DpAK05EkTYOrQVLR1B0TgpCsvYP1LROVa4qL6DbTnpKPoFCvjKbhjs/VGPsLy2fmit5+g==[/tex][tex=14.786x3.0]FCHntSdRHYHvYct0eQKyTAzh4k9igRlYBzr/mnwW9ZoZL/jcTmBDOR9yCihE/2nzX0ItaN8aQqzobCKaeQzqv5eUGbd7ADRItM8/fHiHofPXUx1B2ngI+Q21aBy5x/yjd+HseBuG5n1Ti2BzyeQNKasd7e+BFOs8nSNNQWNG1AU=[/tex][tex=28.5x12.5]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[/tex]所以[tex=12.0x3.5]0Of78XzpFPFjGWxT6yM3gzqc/OGpcPh1jTkTWAlaZ7CPVgbI6lEpCrlM5TTSUq66HK1FDA3Vx+/zBDfiai2yZd0QWxVX3J2XcaKC5qYXdVc=[/tex]，其波形如图所示[img=292x255]178c9ffdc21dd80.png[/img]
举一反三
- 将下列函数展为傅里叶级数：在[tex=3.143x1.357]bvZcHYLryr2+wF1y36oAJQ==[/tex]这个周期上，[tex=5.143x1.357]qAU07a/UMA9qmDdYIFZHiuo1jvRKDnE1dHurpwXBPLY=[/tex]（[tex=0.643x0.786]SPoVA3bJlgfP9Ek9O4AbuA==[/tex]非整数）
- 将下列函数展为傅里叶级数：在[tex=3.143x1.357]bvZcHYLryr2+wF1y36oAJQ==[/tex]这个周期上，[tex=5.5x1.357]UG//YvCBRnNy6A6Xk0Jh192gEj+CV2m18XFGncs4CBA=[/tex]（[tex=0.643x0.786]SPoVA3bJlgfP9Ek9O4AbuA==[/tex]非整数）
- 将下列函数展开成以 [tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的傅里叶级数:[tex=5.357x1.357]6swLeeeQxXKzWtgTVk5Q9w==[/tex]
- 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] .
- 将[tex=4.5x1.357]PaWJa/7BKYvpWZ0AKwXbJw==[/tex]在[tex=2.143x1.357]NAVWPWQ7X2RuKRlMFaIUjw==[/tex]上展开成傅里叶级数。
内容
- 0
把宽为[tex=0.5x0.786]xdTs2QHMXTpKzI7ZnwCRMQ==[/tex], 高为[tex=0.643x1.0]uPu/UBwxTDghY6MHYDLmcA==[/tex], 周期为[tex=0.643x1.0]iollMFTzm3iqFEHRyKQe1A==[/tex]的矩形波（如图所示）展开成傅里叶级数的复数形式.[img=1161x560]179236a68f9d152.jpg[/img]
- 1
把宽为 [tex=0.5x0.786]TTZrOQir/P0Ew6fQBRhcPA==[/tex]，高为[tex=0.643x1.0]8+M7OwdUGZPUoOQAaQHP2A==[/tex]，周期为[tex=0.643x1.0]awBC2UvU2WxG45VihksPuw==[/tex]的矩形波（如图所示）展开成傅里叶级数的复数形式[img=289x139]178bea4c1432f18.png[/img]
- 2
将函数[tex=5.786x1.286]8IPpvasqQdehywWzklHMXYao5nVkJOrW/W8LJZDbT5o=[/tex]在数轴上展开成傅里叶级数 .
- 3
将函数[tex=5.571x1.286]poXx9kzw7gxFgsEa9Qp7sEY4aEblMoGWnnSty8zDy2w=[/tex]展开成傅里叶级数．
- 4
将函数 [tex=5.143x1.5]hlsjkeYAYnrDjeoep69ZLFxvaKcIuunN5lCZgSjd3iI=[/tex]展开成傅里叶级数 .