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某低通滤波器具有升余弦幅度传输特性,其相频特性为理想特性。若[tex=2.643x1.357]XJqGt1Dr5UwO/QYMcsH+bD6IjEGS5u5p9ahI3YjdO1o=[/tex]表示式为[tex=15.429x2.786]u1hILu45PznovWYk6m1MSVgH8z7l8UuzfHI7lpjbgTo4u4P3/7iFhActFlYICk4Pedh/vqK0BP4Auk15PESo0O0qxJEXFcqSzVNmsi8giRsx9L2KQl+gZaaS2o8NtKzRkIRr0uJBvwm9Tu1eU7nc5NWIzR015gy79QV8l5gjQ6E=[/tex],其中[tex=2.929x1.357]hYapsfoNRY685Mlr1aCxGe+Uylk3uHdzXDmPLdlRVlo=[/tex]为理想低通传输特性[tex=14.0x2.429]rI2XnrLSe8CgF4QM2EhBZvoTXbOWkU0PfXWEUvZOOX+SDAGGIRGT74gDz6YqZyDkSFLWuglLG4/+mSy6PF74YiYwhaU1xB+QC89kv/DL6njAcrlt5reV3QI5Ffm5G183C/9ykYv/8LEByNGJUygDcSvgXqP0xwZoMW0dojC5Gbw=[/tex]试求此系统的冲激响应,并与理想低通滤波器之冲激响应相比较。

某低通滤波器具有升余弦幅度传输特性,其相频特性为理想特性。若[tex=2.643x1.357]XJqGt1Dr5UwO/QYMcsH+bD6IjEGS5u5p9ahI3YjdO1o=[/tex]表示式为[tex=15.429x2.786]u1hILu45PznovWYk6m1MSVgH8z7l8UuzfHI7lpjbgTo4u4P3/7iFhActFlYICk4Pedh/vqK0BP4Auk15PESo0O0qxJEXFcqSzVNmsi8giRsx9L2KQl+gZaaS2o8NtKzRkIRr0uJBvwm9Tu1eU7nc5NWIzR015gy79QV8l5gjQ6E=[/tex],其中[tex=2.929x1.357]hYapsfoNRY685Mlr1aCxGe+Uylk3uHdzXDmPLdlRVlo=[/tex]为理想低通传输特性[tex=14.0x2.429]rI2XnrLSe8CgF4QM2EhBZvoTXbOWkU0PfXWEUvZOOX+SDAGGIRGT74gDz6YqZyDkSFLWuglLG4/+mSy6PF74YiYwhaU1xB+QC89kv/DL6njAcrlt5reV3QI5Ffm5G183C/9ykYv/8LEByNGJUygDcSvgXqP0xwZoMW0dojC5Gbw=[/tex]试求此系统的冲激响应,并与理想低通滤波器之冲激响应相比较。

发布时间:2025-08-09 18:57:38
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答案:解:已知[tex=14.0x2.429]rI2XnrLSe8CgF4QM2EhBZvoTXbOWkU0PfXWEUvZOOX+SDAGGIRGT74gDz6YqZyDkSFLWuglLG4/+mSy6PF74YiYwhaU1xB+QC89kv/DL6njAcrlt5reV3QI5Ffm5G183C/9ykYv/8LEByNGJUygDcSvgXqP0xwZoMW0dojC5Gbw=[/tex],则[tex=9.857x2.143]zyBBy3sJx4RQDFqOkmeCYI4ahxhjJKtkLiU5ENommUoPPq3SFbZAh4GwpIc5oqAuCglfxK4vnngvziQ9ePAKbPQe97mzLBzsmE0YesLnYKMa5nTPGpp/jFUjeGcY5R//[/tex]因为[tex=19.214x5.214]l67jpf1vwHfJFXAzDZoY09cwc0Tle57RUsam0CqBXpyLOusCD4eWymwXq2LpQruvkPv0KwmemB0iFpLmC9d4OXohnouDKCEJGJWR/ZomZ1MHwj2WWE30ttH578BRW+733vc8WGbW9LkVbP4JEsuiTgxlW6Hb961KzIy4KMRI3NzJ1PQPRehoPc3kUjKlDkx5DbBrA5Ifa7zhzvPxg024WKC8ieCoyFgJzCtVzhSdzOB4BQJTFSN5Ui5kKLS3MYPKnqWi8OAU3N0qfmfrGSB3CsibbGDYwbqMtnjGbnbEUnKNu/KdMOPzGE4ptk6ITOa6+/qDrMQuwZmykAMv9GkohxefrIFNg5AMpqH7X+ohyDfpkYteINjhrgo/kvzb++3O[/tex]则系统冲激响应为[tex=32.357x9.929]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[/tex]由上述结果可知,升余弦滤波器的冲激响应是将理想低通滤波器冲激响应[tex=2.0x1.357]+L/t1kZaGUZm8Yj1wJPuqw==[/tex]分别左移、右移[tex=1.214x2.143]DipAViX3UcXpPRBOCoMOTupizZIeJ7k7LlfW7nmRX5s=[/tex]个单位后和[tex=2.0x1.357]+L/t1kZaGUZm8Yj1wJPuqw==[/tex]分别乘以相应系数的叠加。与理想低通滤波器相比,此系统的冲激响应也有类似的抽样函数的形状,但主瓣更宽,为理想低通滤波器的两倍,同时幅度减小。
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