求图中周期信号的傅里叶级数。[img=462x215]17a41110c70fcf6.png[/img]
解:图 (a)的三角形式傅里叶级数为[tex=23.429x3.571]cCgmztyAdFZfoxsPt5TUftVIk61Hco0PBnKkT8gJZ88EsAX5FOQz7icyp7oDT9wayoaNtpY1WJh09zGE4OMTZrV6IyHj+uMObBKtjUwyqpMRhjfY4AJ5tOPjsx+z94njm2t6s656GlYtn+GHpZa+8Tyych5yeuZx7suIfQfwBqtBuUieQC26eonILEia4TWScvSfFiLwFSJn5FTd8Yd04n+7aaU09ACNpFrfGa6FHR8=[/tex][tex=29.429x6.786]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[/tex]令 [tex=3.929x2.429]palDt60T1xkPKUnIdrW1FqmGjmnbEvt240dZsk3M55Y=[/tex] 则 [tex=26.214x3.357]FCHntSdRHYHvYct0eQKyTEGQuf6oPP6JWOftW/J1th6BrCsiRNuWMKSbu2OZgOrY85p0vqQGpiKsogAJxyaOrIW+ojQZSeSLunpoMALXO1j7/RDXnA/5f/ZBvNf0zQJzgF5mf04m3whUSqhilmzz13Wsyz1I8vWTK8MRphW1lhk9HpK5hiuYmBV1//aWiBEjJ33h2S4VA40fja21s6SZnCJHMkf/ZDHWuJG2UjkNhi4=[/tex][tex=42.929x3.357]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[/tex][tex=27.214x3.357]BxIppXs3RzPqdDCdNkwS4J7q9MR47BjGNRohQKCZhSgq4rySkaKndR7EK/rN+dGXxbHDqLUfF/D5I4n2yK5Vx+zPwEPmVjIr26/7BLqKlJO+ymrFbU3Hfb+dBjdfZX76awNqTuCJOYD1xOVE80E0IoLIXJUYETOE76R0ga5pDk5qBBdXT9TNlEr9WJ9SAny6DTxusk5QXkdq86BfekAFDrKUcB5pCA6TZldXa1Cxc1MRiUU7KusCL1J8hq3RjGeHRvs4ly+7S5q64zOAkJN69A/GHEjIPDuxO1GDQRTXyoJdez5fdew2vttwaP7aZq1DQJQxICfRVaEBd2hZIVwwtQ==[/tex]在第二个积分表达式中, 令 [tex=3.929x2.429]XQ+Aaf4p8g7vBA213ijZMLZZWEnUTNT2GLl+uxZfEXo=[/tex] 则[tex=32.571x7.071]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[/tex][tex=42.429x3.357]BS3P1u4q94JsSUL+qHGFwc3Y2CSeH1lG6DuftwQtyOlnUEsP6eaSfG77lV4vHm4B54uh4UOVrzBhboTVurTWZswAlGKnV6gZDssAI0se9n5+eDkCZNHBe5Tt+vHMWq0SDVMOgVY1X3c3h2bwW/K2keRhsW2YMIQJYws8YWvE42SqXRmGuYHicw+qQFqFiwuCXHtuCrvBvN+YB/vY2Rq15HWRJDsDem/kzRdcGd8ukmVmUydO61CbVNf1Q6yRlNgOVzDsS8JJza7ecMazt7jwRHG06thHrA1VyYPDWMrNZzcRL/qLIzxzwKJ8T/iTzIW9YCwHEK99kCm10svjGLzeyfwJ24SZy/PwUqda6BBr4YotMiXTNPkAHBYK75GQG7ta/naGXN+bfG7eT/AqLFzqzr5hzBI/Avlit90N/CitERTBc8DvBsS4GlXUwGl7NWeL1Tnkkj3cNFKEzTFsBG7XyTAB6JAWxiFLaEsn3ywGAbY=[/tex]在第二个积分表达式中, 令 [tex=3.929x2.429]e/x8YWxCktOKktxL8VhZ3JMWWq1rgapAhlPIwGGFCTg=[/tex] 则[tex=28.429x3.357]BS3P1u4q94JsSUL+qHGFwe5XREdb3XFmaBlgXeVJ28fzQsfNpICa9qu8VrWp8h7UPpAWVGgQ9+YF/WdBsyD5ODuM+pBqoMsE1a0YZ2jN+48Cm9C55kooi3GtbYuXVxdgObn2xbBnO0QD2yDXbMVfgMf2wpo54wImopD+cGNZT79Y56J5OwgptL700SE95C+YVrc2quzKOxwphwbo3yrN2qIPdH7fIFSJQNaV2bGOlX6Hq+F17Rl/J534k01Zdyl731gkOSjXjX6Y1WLR+N5kbT7jR7Myk6hLG0grafirtdXnPCZG/n4NETmN/3Rhorc6[/tex][tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 为偶数时, [tex=2.429x1.214]28DTK6oiKM40eY0eqc1FEw==[/tex] [tex=0.643x0.786]35ReWWGs/YPu3n9y5K5w7g==[/tex] 为奇数时[tex=32.214x6.643]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[/tex][tex=1.643x1.357]Wfem9oxh0ZS7nZ3KGomKoQ==[/tex] 的三角形式傅里叶级数为 [tex=16.286x3.5]B6nR7zLx1tzkPyP7A9R/MZp6Rn4pGt087JVtzBkr67gJYE3XYvtJgAv1Xcw2ZML2pdCrSM1S0GtL7RgL6SesA0B9Behnpj7dFNksEostRJ54y8beVzQuGQdb9Gthkifg6gXay/yZ9YNIbXcKC1s7Gy/ZKp3cI5WhCWzmNK/ueVI=[/tex] 其中 [tex=5.214x1.214]RvULKWl5idaaBWHhIx/+pBXcyeCrji0zqUmdx/bPRMw=[/tex][br][/br]
举一反三
- 基波周期为T的周期信号x(t)的复指数型傅里叶级数表示为[img=286x83]1803110fbcee2b6.jpg[/img],其中[img=38x29]1803110fc57ea57.png[/img]是傅里叶级数系数。
- 基波周期为T的周期信号x(t)的复指数型傅里叶级数表示为[img=286x83]1803243c2780ec0.jpg[/img],其中[img=38x29]1803243c30c5376.png[/img]是傅里叶级数系数。
- 连续周期信号的傅里叶级数系数[img=38x29]1803243c399defd.png[/img]是离散非周期的,而离散周期信号傅里叶级数系数[img=38x29]1803243c399defd.png[/img]是离散且周期的。
- 求图所示周期三角信号的傅里叶级数并画出频谱图。[img=347x137]17a564a6989bbeb.png[/img]
- 求图示周期矩形信号的傅里叶级数(三角形式与指数形式)。[img=601x265]17a3e3d3cb26c67.png[/img]
内容
- 0
已知连续周期信号 f (t) 的波形如图 3-58 所示。求指数型傅里叶级数; [img=496x170]17ae5c56171a2b3.png[/img]
- 1
令x(t)是一个基波周期为T的周期信号,其傅里叶级数系数为[img=17x17]1803243be68ec81.png[/img],则其实部[img=74x29]1803243befc5ec2.png[/img]的傅里叶级数系数为( )。 A: [img=148x74]1803243bfbdc29e.jpg[/img] B: [img=161x72]1803243c05e0ae2.jpg[/img] C: [img=162x78]1803243c1173178.jpg[/img] D: [img=180x76]1803243c1c16ccf.jpg[/img]
- 2
若周期信号 是实信号和奇信号,则其傅里叶级数系数是:( )[img=61x43]17a411ddfb9903f.png[/img]
- 3
为什么连续周期信号的傅里叶级数是无限项级数,而离散周期信号的傅里叶级数却是有限项级数?
- 4
利用周期性矩形脉冲与周期性三角形脉冲的傅里叶级数展开式(3-30)及式(3-38),求图3-10波形所示信号的傅里叶级数。[img=408x205]17d575890c0e721.png[/img]